Dolphin Subscription mod on market does this. and a whole bunch more!
You can set it to force members to select membership level on joining, charge what you want for it, set what membership level (s) can do on site. It will even automatically take payment the next year, or whenever you define in settings. Very very good mod. DOlphin standard payments will not automatically take ongoing payments, just one off.
Mod is by martinboi, also costs less than your quoted budget.