I would forget aiming for 300bhp, really the best way there is to stick a 20vt engine into the back of it. Certainly possible for £10k if you can fabricate, probably not if you are just going to pay someone to do all the work. Plus you said:
somewhere in the 200bhp region and then chasis work or 300 bhp and work slightly on chasis
300bhp would demand significant work on the chassis or you'd be left with a death trap of a car or at very least a car that would simply rip itself to shreds every time you floor the throttle. Yoof has just over 200bhp and I have just under and we have both spent a significant amount (time and money) on chassis strengthening and modifications just to cope with that much power. A mk3 polo chassis is essentially a modification of the original design for the mk1 polo, so it's early 70s technology and was probably drawn up with about 70bhp max in mind. So don't underestimate the amount of work needed to end up with a usable, reliable car after getting to the 200bhp point.
I can't speak for yoof but I know that if I were to simply pay for someone to do all the work I've done on my car then it'd easily cost £10k.
Replacing destroyed gearboxes is par-for-course on a high power g40, you'll just have to get used to it. Or spend £10k alone on a fancy S1600 6n2 gearbox. I currently have 3 gearboxes, one is awaiting a rebuild (wont go into 1st any more), one is on my car and one is a spare. I've also got a collection of dead gearboxes and a snapped in half LSD.