"$500"
The way I see it, you get what you pay for with bikes.
either buying something new and expensive that works well
or something used super cheap then pouring money into untill its fixed
either approach, expect to spend about the same in the end if you want a good ride.
of course the exception to that rule, is if you know what you're doing mechanically and can fix things yourself and have access to parts. Then the former path of buying cheap and fixing has significant savings.
That doesn't apply to you though.
Support the shop, have them do the repairs.
60$ for a bottom bracket replace
100$ to replace the damaged rear wheel (leave the front wheel alone if its not a problem)
30$ rear brake job
well, maybe not the shop you described, since their bid is too high
but some shop someplace that matches those prices is a good value.