TBH its surprising what you can run with okay. We got a 3-wheeler years ago which was a return from Mothercare. It's pretty heavy, and only has 12 inch wheels, yet I've taken all 4 of our kiddies out in it, up to a pretty hilly 10 miles or so.
You must make sure it has a fixed front wheel. (I mean, it must go round, obviously, but a lot of 3 wheelers not designed for running have one that will swivel - I wouldn't even trust one which has a locking mechanism).
Check the height of the handlebars - with the fixed wheel, unless you are just doing a very gentle curve, which you can just do with sideways pressure, you will have to lift the front wheel - my wife finds this difficult as she is quite a bit shorter than me.
Our local shop let me take a few out for test-drives, though we had built up a pretty good relationship first. I'd be wary of buying one online unless you are sure what you are looking for.
The other thing to bear in mind is will you be wanting to cart it anywhere in the car. Bigger wheels may make running easier, but then you'll need a bigger boot to tranport it.