Shonee, you didn't make it plain in your post that you are a 5ft8 , 20 stone/280lb - woman. You are a big girl that's for sure.
Finding a horse which can carry your weight won't be too difficult - any of the
Draught breeds should be able to carry you at the walk and trot.
A Shire, a Clydesdale a Suffolk Punch, a Percheron will all be up to weight
And they will usually stand at around 16 hands. As for price well, you'll get what you pay for.
However. A big draught horse is a lot of hairy beast to manage. If they want to go to the right, then off to the right they will go And if they don't fancy moving at all then you won't get them to move. As for jumping and dressage, well they are not the breed to choose.
These heavy horses are special and you ask them to do as you wish - you can't demand. Communication skills are everything.
Now before you rush off and buy what can prove to be a very expensive animal to feed. May I suggest that you ask whoever it is teaching you to ride to discuss with you what sort of horse will suit your level of riding skills.
There are a lots of trekking centres in Wales. Get on the phone - you tell them about your size weight and experience and go off for a week to ride whatever horse they reckon will carry you. Some centres will have a rider weight limit of around fourteen stone but much will depend on your level of riding expertise.
You never know, they might even sell you a horse.