omg yes, as PP said, the very first thing you should do it read the dodgy dealer pages on FB. A good dealer are worth their weight in gold and there are lots of good ones. But the bad ones are plentiful too.
Look for a schoolmaster - don't even look at anything under the age of about 8 - it just won't have the experience you need as a novice owner.
Don't over horse yourself, be realistic about your current capabilities and what you actually want to do. I.e., don't be drawn into buying a flashy sports horse if what you actually want is something safe to hack and do low level schooling/competing.
Be very careful - it's an absolute minefield - so many dishonest sellers out there. Everyone is selling for a reason, you need to decipher if their reasons for selling are genuine.
If you're a small adult it's worth having a look on the pony club website - some of these ponies are worth their weight in gold and ARE being sold for genuine reasons - i.e., they've been outgrown.
If you haven't already, go and scope out all of the local livery yards. Make a list of what you want and what you're willing to compromise on.
Cost out absolutely everything before you start looking. Livery, shoes, wormers, vaccinations, tack, rugs, equipment, insurance, feed/hay if not on full livery, lessons, competing etc
Having owned several horses in the past I can tell you it's a bloody expensive hobby. I've had a few years away from horse ownership and was in the position to get another one this year. I've decided against it! I don't want to put you off, but it makes my eyes water when I think about how much money i've spent on horses over the years!