Any of the basses mentioned above would be a good place to start. The Squier Jaguar SS is particularly nice for small hands because the neck is so thin. The Mikro is also a good choice. Both are available new for under 200 bucks and can be gigged with no mods. If you can find a used Gretsch G2220 grab it.
One thing I will say, having been in almost your exact situation when I started playing bass 6 years ago: If you are already thinking of a short scale due to potential physical constraints then go with one. A lot of folks will try to convince you to play a 34". Don't listen to them
One thing I will say, having been in almost your exact situation when I started playing bass 6 years ago: If you are already thinking of a short scale due to potential physical constraints then go with one. A lot of folks will try to convince you to play a 34". Don't listen to them