The only problem with this is that Engine Upgrade only comes on two 30 dollar ships, (YT-1300, YV-666) neither of which are Imperial.

On a budget, considering that the topic-starter wants to play Imperials and sometimes Scum, that's the cost of two of the smaller fighters for an incompatible ship (YT-1300), or a heavy commitment to Scum (YV-666).

As you said TIEs are a solid choice.

Even if you are a regular tourney player, 90% of your games will still be casual - so buying expansions purely for cards is unnecessary, especially in the early stages of getting a collection together.

If you haven't got a particular card just proxy it.

Definitely another vote for the Firespray - not super competitive but solid, a decent all-rounder and works for both factions you're interested in. You'd be silly not to get it

Brand new to the addiction... i mean hobby. Just got a core set. Watched gameplay this past week at my local game store. Def want to play imperial and possibly scum. Any help on what to buy next would be appreciated. I am on a limited budget.

Put it down now, before it ruins your life forever. Once you start using words like "meta" and "squints" and "superdash", forever will it consume your destiny.