Ideally you should try various bikes out but this is a problem because you won't find many (if any) small bikes in dealers. In the end I relied on the experience of the chaps in my local bike shop. If you have a bike at the moment you know how high you have the saddle so you know perhaps the most important part of the geometry. You also have to watch out for how high the crossbar will be as that could be inconvenient to say the least.
I'm 64 and 5' 2" and I ride a Cube Acid which is a 29er with no problem. I must confess I never thought I would end up with a 29er with my little legs but it is fine. I find the 29er is a much better ride than my previous (manual) bike which was a very good quality bike in its day but has 26" wheels. Obviously I have the smallest 15" frame on my Acid. I had to have the end of the seat post sawn off so the seat would go low enough (the down tube has a bend half way down )and I don't think I would be able to fit a suspension seat post for the same reason. Apart from that it has worked out great - I have done 1,400 very happy miles so far.
Some might say the bike looks a bit odd with the handlebars higher than the saddle but, at my age, I've found I prefer the more relaxed riding position. So I recommend you look into what bikes come with very small frames. Of course your budget and cycling needs are important considerations. The Acid Allroad which is what I have now comes with the Gen 4 Bosch CX and the rrp is £1,999. You might be able to get a little discount on this price. Although they aren't sexy I do like having proper mudguards as they offer pretty good protection. Also, although I never ride in the dark, the built in front light is useful when going through trail tunnels. The rear light is of no use whatsoever to me.