First handgun, $400 out the door for a used SA Ultra compact. First new handgun, $300 for a Ruger LCP.
As far as how much to spend on your first one, spend as much as you have to to buy what you want. If you arent happy with the first one, there will always be more down the road. My wife started out wanting ONE for personal protection, and that was about the extent of her interests. I think at last count she had 12 of her own, and still looking any time she gets near a gun counter..
First one I bought was an FEG hi power clone. $200. Year was 1996. It shot good and was reliable but my friends made fun. Traded it towards a Walther PPK/s.
OP buy what you can afford. If you go cheap you may wish you didn't. Get something you will enjoy and take pride in owning.