Personally, I purchased a folding wheelchair with small wheels (I think they're called attended wheelchairs). It cost me £100 or thereabouts. If I was pushing it a lot, I think one with a motor might be a good idea. The only slightly odd thing I've found is that it seems to me the handles to push with are a little low, and I'm only 5' 5". Possibly I have extra short arms or something!
I bought one for mum which has the small wheels and 'soft' tyres so nice ride for mum. Useful features bar either side of wheels to push down on with your foot for going up steps (saves on the arms), brake is on the handles, foot rests swing out so mum doesn't catch her ankles getting in and out. Back folds down, and foot rests come off, all which helps it to fit in the boot of my small coupe car. Bit pricey at around £195, but hoping to have many miles out of it.
PS Also bought one of those waterproof capes.
Cate's sounds identical to the one I purchased (except for the brakes), but mine was a reconditioned rental once, hence the price difference. I like the sound of the brakes on the handle, though. The foot operated one can be a bit of a pain when you're in close quarters, like getting into a car. I bought mine from fred walton, but I'm sure there are other sources. Don't forget, you can aslo get them from the red cross on long term loan.