Hey there. I will say that you have to understand of coure that Trek itself had never been conceived opf before. You'll notice some small inconsistencies here and there, but considering that it was the first time they were trying it, it holds together really well.
The important thing is the characters. The main characters knew their roles instantly. From their first frame of film which tehy are on creen togethe, there is a chemistrry between Kirk and spock that has since been unrivaled in Television.
Also look past the effects. I actually think tehy are quite good, but obviosuly the technology and budget were limited. Let your imagination complete the picture the effects were trying to create, and give kudos when the effects truely work, and you'll find that more often than not they will work.
Also keep in mind that TOS is Roddenberry, and Gene Coon. The ran the show. Rodennberry had a true vision into human potential and that we can all have a function. Notice a female African American in an important bridge role on a show produced in the 60's Gene Coon brought drma to Gene's vision, helping to fill in the details and give the ship a mission from wek to week.
Also many episodes are allegories to events that were happening at the time that most shows couldn't talk about, but the networks missed it with Star Trek, and they didn't see the allegory. Makes for an interesting take on the show.
Most of all, enjoy at as good campy fun. Embrace the overplayed music, the occassional over acting moment,. Treasure it, because in modern shows we've become too cynical to enjoy such things.