Nancy, I’m a bowing (and plucking) double bassist (and electric bassist before that, to give you some context) who has been in the same situation.
1- DB vs violin or cello bow?
Physics mean that the speed with which you move your bow have an impact on loudness AND pitch. So a violin requires faster and longer movements with the bow because of its higher tuning, while a DB requires slower movements, hence the length difference (as well as the overall build strength - as raised before on this thread, you let your DB bow rest more on the strings so it needs to bear your arm’s weight).
2- “German” or “French” bow?
It’s a matter of preference AND teacher availability. Both bows have completely different holding techniques and moderately different movement / bowing techniques. A (competent!) teacher for one type of bow will be understandably reluctant to teach the other style. UK teachers and orchestras tend to prefer the French bow. However, both bows essentially sound the same and can do the same things.
if you don’t know and don’t feel strongly drawn to either, go for the type that matches the teachers you can get. Unless you have existing wrist and arm problems in which case one type of bow might suit you better over the other type.
3- price?
Around £100-200 for a starter one. I appreciate it’s not as cheap as a normal person would imagine but a bow that’s too cheap will definitely have balance issues and give you bad habits.
Last point: please please please get a teacher. Bad DB techniques can ruin your hands and wrists and severely limit what you can do with the instrument.
Best wishes.