Just a bit more to reinforce the good advice that has already been posted:

I'm 5'1" and my Rodriguez is effectively 43cm with 650C wheels. It still has a bit of toe overlap, but I never turn that sharply. The bike it replaced was custom for its original owner, 42cm also with 650C wheels. Both are steel, smooth rides.

With your budget and needs you really should consider custom. Find a fitter you like, ask them how long it takes them to fabricate a bike, how many adjustments they will give you after delivery.

Hopefully with the right bike you'll be able to stay limber and hold off that arthritis a bit longer!