I just got the core set, what imperial ships should I get to build my fleet?

Grab an ISD, a fighter pack and a Scum & Villany pack. Most folks will tell you to grab a Gladiator for certain.

After that? What ever you like the look of.

Agree with Dan's priorities: if you're looking to get just one ship up front, get an ISD, which will get you to a usable 300-point fleet on its own. Next get either a Squadron pack or a GSD, either one of which will get you to a viable 400 point fleet, depending on whether you prefer to play squadron- or ship-heavy.

From there, pick up one of each of the Imp expansion packs, and then one of each of the Rebel ship packs, probably starting with the Nebulon B and the MC30 (they come with some upgrades that are really good for you).

By that point, you should have a pretty good idea of what you like to play and what you want next.

Welcome to the game, you vile oppressor!

Thanks to both of you, this is really helpful.