Check this place for your bikes: http://www.tartybikes.co.uk. Easily the best place in the UK to buy the gear from. (If you're from here)
£500 budget is a good place to start, I got my first 20" for about £400 new, and it was a belter, so have a look around on Tarty. Obviously it'll make a huge difference if you go second hand as well.
In regards to brakes, there is a massive argument as to which is better but a good set-up is key to most of it. I've personally run hydraulics for all of my bikes and I've never had a single problem, but other people run into loads of problems and go to vee's. And vice-versa. If you're used to one more than the other then I'd stay with them. But if you like the idea of going for a different setup then do it. Obviously I can't comment on what vee's are like trials-wise so I'll leave that up to someone else, but hydraulic Magura/Echo and the likes are brilliant... oh and brake pads can make or break it (no pun intended).
Hight wise, it might be worth trying one out (if you can). Where abouts are you from? There's loads of members on here so I'm sure one will be near you? Other than that I've ridden with/seen loads of guys/girls riding 20" wheel's and they've been +10-15cm taller than me. I'm 173cm. Sorry if this has confused you more. :$