I've only played a bit of ship combat, and I haven't tried building a ship, so take this for what it's worth...The combat we did was in ships with balanced armour, defenses and shields. Obviously sacrificing one of those makes the ship more vulnerable but I don't know which is most important.
I think you'll struggle to come up with a low-budget ship that does more than one thing. Look at the Kevolari Venture in the book, as an example of a basic ship: tier 1, 6 crew, all the normal ship stuff, 2 weapons, and a science lab. Basically, it has one special feature, the science lab. If you want more useful add-ons it'll cost more.
Maybe you could look at the sample starships in the book and find one with a similar amount of "stuff" as what you want - not the same in detail, just a similar number of weapons and filled expansion bays. That might give you an idea of what you can get for your money.
Also keep in mind that you can upgrade your ship later, within the limits of its frame. Your ship wouldn't be able to do everything from the start but would improve over time.
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