Getting something to suit your current riding ability and to meet your future needs is probably the first thing to consider over the actual size. I think you would have a lot of fun if you got a forward going welsh cob type around 15.00hh, provided you are capable of [and would enjoy] riding such an animal. If you are more of a novice then you need to find something with a calm and kind nature to be your schoolmaster.
Something which is more of the pony type rather than a horse type will be good for PC and will be up to your weight, in fact almost any horse/pony [not Welsh A or B obviously] will be fine for your weight.
For some jumping classes there will be restrictions, but others will advise, however there seems to be a lot of pressure to buy a horse, and I would advise against this, a pony type is often more sound, less complex, more fun, but can be cheeky.
I would advise a five stage vetting, and be prepared to take regular lessons as it is all too easy to bomb around and forget the basic training. For eventing it needs to have nice paces and be capable of jumping a variety of jumps, plain and coloured.
There are loads of posts on what size just now! Temperament and suitability for the job are far more important than size!
That said - I would tend to echo Bonkers2 in opting for a pony rather than a horse, or at least not ruling one out! PC don't mind what size your animal is - but other disciplines do. For showjumping, for example, if you have a pony below 148cm (14.2hh) you can compete in juniors against other kids. If the horse is over 148cms you'll compete against adults who have miles more experience (and money!) which can be demoralizing. Plus you can get access to the Junior Academy training. For eventing it is less specific - the pony has to be over (I think) 13hh. But you won't want anything that small anyway. You can event to quite a high level on a pony - look at Headly Brittania!
In general terms pony types are hardier, cost less to feed, are more versatile (having tended to be bred as all-rounders) and are easier to mount from the ground / handle in the stable. They can be cheekier - I think they tend to have more personality than a bigger horse. But there are always exceptions!