So, what am I saying? Well without trying to be patronizing gut the lot, then I'd say go for stickier tyres. I think you'll be hard pressed to find one that looks as good as the one in the original post for that kind of money, so f**k the bodywork, it'll no doubt pick some battle scars up anyway. Just make sure the mechanicals are sweet. But anyway, stripping the car should be mainly free so let's theoretically say it costs £0
Some decent 'fast road' tyres, let's say, Toyo T1Rs would be around £350 a set
Then I'd say get some good lowering springs, a strut brace and anti roll bars, these would probably be around £600 all in
I'd probably upgrade the brakes at this point, unfortunately I don't think the Almera GTi has a great deal of aftermarket support, but I found a set of 4 grooved brake discs on eBay for about £150. So...
This is the fun bit, power, with this much money you could probably do a home-made forced induction conversion or just buy an SR20DET and fit that.
Of course it all depends on how much access you have to tools and facilities, and how much experience you've got. Once again sorry to sound patronizing if I do but this is probably one of the ideas I like most on PCA, you got Facebook?
Ps: I just saw the car in the OP on Pistonheads for £600, I stand corrected