I want a small imperial ship. I currently have the Slave 1, Tie Phanthom, Tie Defender, Core Set, and Force Awakens Expansions. I am mainly considering the Tie Interceptor, Advanced, or Punisher. Thoughts?

Go for an Interceptor at first. They come with some interesting pilots and the great fun to fly. Real slippery arc-dodgers. I've got the other ships you mention and by far my Interceptors would get the most table time. They can be a bit fragile, but no more than a TIE Fighter. Plus three attack dice is always good. The Advanced isn't bad, but it really does require the upgrades that come with the Raider to help make it more effective. The Punisher comes with some interesting upgrades, but it's probably best to get that after you've got a regular TIE Bomber as well. Then you will have a good selection of bombs and mines to choose from. Of course the humble TIE Fighter expansion will never be a bad investment as it comes with pilots and upgrades that aren't in the core set.

I'll probably end up going with the Tie Interceptor. Thanks for the info!

Tie advanced are good with the cards from the raider but not on their own, so you either need to proxy the cards or pay for a raider.

Interceptors are a sound choice.

If the budget stretches, try for Imperial Aces, there are a bunch of great upgrades there, which will benefit your lists tremendously.

How about the good old TIE expansion? You get Howlrunner. She is very very good and you can always use more expendable fodder as an Imperial player.

For Howlrunner, I don't really want to get into buying 4 of each expansion, so thats not a priority. Imperial Aces on Amazon is on sale so that's something.

A mini swarm of ties is not a bad thing to own.

Try and budget for a new ship and a TIE Fighter at the same time. That way you'll build up the fleet with a decent amount of interesting ships and a good amount of basic cannon fodder ships.