Zen is the Game Store, called C-Store, currency used in all Perfect World games.
There are 3 ways to get Zen:
Purchase directly with real money and then transfer it to the game to make a store purchase.
Do those surveys advertised on the homepage/forums to get free Zen, though those could be called datamining traps for the most part.
Earn Dilithium in game, which might be hard at the beginning, and use the Dilithium Exchange to convert it to Zen.
Right now is a great time to do that, as Zen are cheaper then ever before on the Exchange, since Dilithium is becoming more and more valuable in game, it is also used to purchase high end gear and progress Fleet Starbases and such.
There are a few things you might want to buy from the C-Store:
Energy Credit Limit Upgrade, I think right now you are stuck at 10 million max, which sounds like a lot, but is really not if you want to purchase high end gear later from the EC Exchange. Upgrade ups it to a Billion or so.
maybe a couple of character slots if you plan on creating more alts. Atm you have 1 slot for your Fed and as soon as you reach level 25 you gain a Klingon Character slot.
Eventually you might need more Inventory and Bank slots. I have maxed them on my Main and I am gold, so I have more than a silver player by default and I am still constantly out of space to put stuff in.
If you hurry and get to level 10 or so you can still participate in the Winter daily in Q's Winter Wonderland to earn a free endgame Breen ship, which has better stats then any ship you get for for free through standard progression and leveling.
The Miranda Class is the standard starter ship, it is also possible to buy a classic Constitution class, an Oberth class, and an NX class in the C-Store to start with after the tutorial or you can get the Steam Starter Pack, which includes a starter level and an endgame version of the Steamrunner class.
Every 10 ranks you earn a new more powerful ship seperated by Tiers (1-5), which have typically a C-Store variant that has mildly better stats and mostly comes with a special powers console.
Endgame is dominated by C-Store ships , Fleet refits and Lockbox ships, but minus some nifty gadgets the standard free T5 ships are mostly competitive, so no pressing need to buy one.