If there is a new series it should be a remake of the entire franchise - alternate timeline with a different enough plot to make it both brand new and familiar, and I'd rather they'd cut out the Human-form Replicators and the Ori. Also, the Replicators are primarily the Asgard's enemy, so no need to obsess over them. Lastly, some more consistency and realism, while still maintaining the spirit of the entire franchise (except SGU), which is to be fun and not take yourself too seriously, while still dealing with serious issues and having a serious plot. The main character could be serious, like O'Neil from Stargate, or a clown like O'Neil from Stargate SG-1, it doesn't matter. Example outline of the series that I thought of (merges Stargate SG-1 and Stargate Atlantis):
Movie:
As seen, with some improvements.
Season 1:
Apophis moves in to Ra's former territories, notably Abidos. Apophis interrogates them about the death of Ra and the source of their new weapons, but even though many break under the torture they are unable to betray Earth as the ones who were captured and interrogated don't know the gate address, symbol, or any other identifying information (Skaara and Sharei are in hiding, and are the only ones who know). Apophis vows to find and destroy the insolent humans before they become a real threat. After Apophis leaves the people of Abidos call Earth for help. America then searches for Apophis with the intention of stopping him at any cost, and they eventually find and kill him with the aid of Teal'C. It's obvious that Klorel intends to find and destroy Earth.
Season 2:
Klorel spends a whole bunch of time establishing control of his (permanently) deceased father's troops and defending his territory. In the mean while, America is doing everything it can to acquire the capacity to defend itself, and with the intelligence provided by Teal'C they manage to steal a small fleet of Goa'uld ships (Alkesh and scout ships, which are then modified by Earth for use in battle), killing several minor Goa'uld in the process. Klorel discovers one of Earth's off-world bases and sends a small yet sufficient force to attack it. The base is defeated and destroyed. Most of the personnel manage to escape, but many are killed and a few are captured. Klorel interrogates them and discovers Earth's location, but can't do anything about it yet as he is still engaged in heavy battle against his rivals.
Season 3:
When Klorel finally does show up with a small fleet (the rest are needed to defend his holdings) they manage to surprise and defeat him, but only at a great cost. He escapes and hides on Earth, and calls on his forces to come rescue him. Klorel is captured, but then his army arrives. He is used as a hostage to keep it away, but his troops sneak back and rescue him. However, word of his defeat and capture reaches the other Goa'uld, who quickly seize the opportunity to attack his territories. Klorel is forced to occupy himself with the defense of his territories, but he does not forget Earth. In the mean time, many countries on Earth know about the battle, and an alliance is formed for planetary defense. Earth scrambles to rebuild its fleet.
Season 4:
Earth begins experimenting with its own battleships, still scrambling frantically to build a military force capable of repelling the Goa'uld, and capture several Goa'uld ships to add to their fleet (which is made of modified Goa'uld ships and cobbled together Earth ships with Goa'uld parts). The secret gets harder to keep, and some governments outside the alliance are going public, but skepticism still carries the day. Earth gets its hands on important intelligence and manages to catch Klorel with his pants down, capturing him and several Hatak while destroying several others (big battle included).
Season 5:
The collapse of Klorel's empire finally gets the full attention of the System Lords, but they are all too busy squabbling over his armies and territories to do anything for a while. In the mean time, several countries around the globe complete the first batch of X-303s and X-302s. The System Lords finally form a coalition against Earth. Earth does what it can to destroy the Goa'uld fleet before they reach Earth and to acquire new ships, but they come anyway and defeat Earth's fleet. However, the System Lords only sent a fraction of their forces to attack Earth, and those are weekend enough by the battle that they are unable to defeat Earth's ground-based defenses and are forced to retreat. (in this story, Earth's nukes are powerful enough that a small barrage can destroy a Hatak, but the Hatak can shoot down the missiles before impact. However, Earth's ground-based defenses are capable of shooting hundreds of missiles at once, and also include energy canons salvaged from wrecked Hatak vessels as well as other means).
Season 6:
With the great battle that took place the public pretty much knows what's going on, but they don't truly believe it since the governments of the Global Alliance (which has expanded) still deny it. With the loss of a fleet of ships large enough to be the army of a System Lord, the System Lords are seen as weak, and with the huge egos involved there is much blame being flung around, while lesser Goa'uld see this as an opportunity for advancement. The Goa'uld empire plunges into Chaos. It is under these conditions that Anubis makes his covert comeback, conquering many lesser Goa'uld with his superior ships and super-soldiers. He then joins the ranks of the System Lords, only to declare war on them.
Season 7:
Earth has rebuilt its fleet, and it's bigger and better than ever. They ally themselves with the System Lords and after a war that lasts a whole year, they corner Anubis and defeat his army, but he and his most loyal followers escape, and he still has many secret bases remaining.
Season 8:
While hunting for Anubis, the Allies fight over what he left behind, especially the technology. Anubis resurfaces faster than they thought, and quickly manages to gain control of a vast fleet once more, all thanks to the Allies lowering their guard and fighting amongst themselves until it was too late! Earth learns that Anubis is looking for a stash of ancient weapons. Turns out it's on Earth, and Anubis comes to get it. A great battle ensues, ending with an overwhelming victory for Earth as they manage for find and use the weapon shortly after the battle has begun. Now that Earth is truly secure from attack, the Global Alliance goes public with most of the story, but hides the existence of the Stargate. Anubis is still out there in orbit around Earth, although everyone believes he is dead.
Season 9:
The System Lords resurface to take control of all that was held by Anubis, clashing with Earth and other groups that have come to claim the abandoned lands and armies. The Jaffa who served Anubis are confused, and many become open to the idea that the Goa'uld are not gods. The seeds of the Jaffa Rebellion are finally planted. The System Lords have by far the greatest armies, although Earth is the second super-power, with a fleet to rival any individual System Lord and an unbeatable weapon placed on Earth, rendering it untouchable to conventional attacks. Multilateral war ensues over Anubis's legacy, while Anubis himself plots his comeback - to take over Earth from the inside. Anubis's plan is foiled, and he is forced to flee Earth. Earth discovers the Ancient city of Atlantis and sends an expedition to explore it, while Anubis infiltrates Tolana. His presence is quickly discovered and he is expelled, but not before getting his hands on some interesting new technology. (No big battle to mark the end of the season this time, but plenty of nice battles throughout the season).
Season 10:
The Atlantis expedition accidentally awakens the Wraith, starting a whole new war with a whole new enemy. As the Wraith amass their forces, Earth amasses its own, culminating in nice big bloodbath in the Pegasus galaxy. In the mean time, Earth is still fighting a war against the Goa'uld, Anubis is building a new force, enhanced with some stolen Tolan technology, the Jaffa Rebellion is growing, but being strongly targeted by the System Lords. A whole new galaxy is being explored by the Atlantis expedition team as they prepare for battle.
Season 11:
The battle of Atlantis is won, but the Wraith have what they are looking for: the location of Earth. They are now preparing an invasion force. In the Milky Way, things couldn't be worse: With Earth suffering greatly from the absence of an entire fleet sent to combat the Wraith, the System Lords are making great advances, but as their lines stretch thin, Anubis makes yet another comeback. With a fleet markedly superior to his previous one, he once again builds a vast empire, and the System Lords and Earth are both weakened and on the retreat. With Anubis returning Earth once again forms an Alliance with the System Lords, as well as some other forces in the galaxy. The Wraith arrive at Earth and lose big, but they retreat to begin establishing a long term presence in the galaxy. The Allies and Anubis enter a de-facto cease-fire.
Season 12:
The groups who form the Milky Way Alliance are in a state of low-intensity war with each other, while the Wraith are increasing their foothold. A war encompassing 2 galaxies begins in earnest, and rivalries and politics are amazingly put aside to combat a foe who sees everyone else as dinner. The Wraith are finally beaten out of the Milky Way Galaxy, but that just causes the shaky Alliance to collapse as Anubis turns his attentions back towards expansion, and everyone else towards resisting him. Back in Pegasus the fight is far from over, as the Wraith engage Earth's forces in several battles over the control of various worlds. Earth's forces are severely outnumbered, resulting in several defeats and culminating in a second battle of Atlantis, which is again won by Earth, but this time with almost only the power of the city, as the fleet has been cleverly diverted by the Wraith to do battle elsewhere. Earth is left with nothing more than a token presence in the Pegasus galaxy, just as the Wraith have nothing more than a token presence in the Milky Way galaxy.