For a first time owner and budding modifier, a more common car would be easier to work on. Preferably one with a manual transmission.

An SiR isn't actually a bad choice, but sort of out of budget, and chances of finding an unmolested one are slim.

Other candidates within the price range with moddability, likely first-generation Jazzes, though the most desirable one, the 1.5 MT, is very rare secondhand... don't get the CVTs. For a first car, a first-gen Jazz can teach you a lot about driving. It's light, nimble, stable and a joy to drive. Only weak spots are the sucky electric power steering (sucky in terms of feel) and the suspension bushings.

Secondhand Miata might just fall into your price range at this point... but the local supply is very old and will require lots of work. Fantastic cars to drive, but local ones have the detuned 90 hp engine, so they're going to be slower than a Corolla before modification. Definitely more fun, though.

I'd suggest a Lynx RS, but that's just me. Fantastic steering... Bimmer-like, actually... and it's nearly just as quick as an SiR, and better loaded. But the engine is a limitation in terms of modification (unless you turbo... but that's not for newbs). For a first-time driver, though, that's not a bad thing... you can focus on the parts of the car that actually matter... suspension, brakes, etcetera.

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In the 200-350 price range, there are tons of cars you can work on.

"Classic" Minis... 250k-350k.... (lovely little cars)... since there are 93' and up models available, these will not be in bad shape and can be driven right after being bought...
VW Beetles... 50k-150k... ...huge enthusiast support group.
89-92 Corollas... 100k-150k... (fantastic variety of modifications... 4AGE, 4AGZE, 4AGE 20V... etcetera... available)
Sentras... best bet is the 98 B14... 150k... add 60k for an SR20DE swap, or buy a swapped car for 150-200k.
Toyota Echos... 250k+

or even 70's Japanese and European sedans like the Corolla Sprinter or Ford Escort... starting at 10-50k... but these will require a LOT of work... and will spend a lot of time in the garage before they're in running condition. I'd suggest a Nissan 510, but these are super rare and you might spend up to 100k just to buy one in crappy condition.