"A guitar".
Classical, acoustic or electric?
[br]What is your primary musical interest genre?
5'3" = petite female given the name? Probability is also smaller hands/shorter fingers (assuming proportionality). Take that into consideration when you buy.
General advice.
Importantly, you want a neck profile and body which are a comfortable fit, so after you get some recommendations, best that you try on for size [u]before[/u] buying. Buy for fit & intended purpose, not headstock associative status or looks.
I'm a Yamaha advocate (no quid pro quo association). They have been making musical instruments a long time, make some superb in high end professional instruments, but apply their same traditional Japanese pursuit of perfection in everything they do ethos to their affordable entry and intermediate tier segments. Importantly as far as you're concerned, their designs aren't stuck in the 1950s catering to consumer resistance to change, which along with an international and emerging Asian market demographic growth potential of the new century, sees them produce guitars orientated to people of that physical build and stature.
With £500 quid, you have a considerable purchase option largesse.
Electric. A little over your budget, one of these, (in black here & a litttle cheaper but an online distance order) would take you into forever and cover almost anything you want to do with electric except trash Metal. Alternatively within your budget with cash to spare, one of these will serve well for a decade plus as well. Many pub circuit pros use them as stage gutiars. I have both and can vouch that they are great instruments, full scale Alder bodied, yet perfect for the smaller handed person. Yamaha genius.[br][br](e-)Acoustic. Right on budget a beautiful quality instrument in this. The only limiting factor with this instrument for many years will be the person playing it.
Again marginally over your budget, this is more to my liking and will probably be my own next e-acoustic. Well within budget is this. I own one and would buy the same again. Fast neck, low action, comfortably fitting body, a delight to play.
Of course, choice just abounds. Takamine, Cort, Harley Benton, Tanglewood take your pick. Here's a good place to window shop from the UK to get an idea of what's available and narrow down the choice or become even more confused - strike out as applicable. Lots of places to buy locally in the UK including well knowns such as PMT, Andertons, Gear4Music.
Happy hunting. = ]
manXcat