In my experience the cheap wheels that I've gotten for some repairs or just because I'm being cheap all needed to have the spokes stress relieved and re-tensioned and trued again right out of the box. Buy a $35 new wheel and you'll very likely be right back where you are now within a few months at the most if you ride often. Spend that same $35 to have a shop that knows their stuff replace the broken spokes and any dodgey spokes with new ones and properly tension and true the wheel and it'll be reliable for years to come.

Often bike shops build wheels during their slow times. If you can get a budget wheel that was built by them it will likely be tensioned and trued to a much higher standard than the Amazon factory machine built wheel. It may cost you $15 bucks more but the money would be well worth the extra reliability. If you can find such a wheel or buy the new wheel from the shop and talk them into stress relieving going over the tensioning of a factory machine built wheel from them for an extra $10 you'd be far, far ahead of just pulling one out of a box and thinking that you're done. Such machine wheels WILL "settle" and need re-trueing and re-tensioning as they stress relieve themselves in use. Ignore that fact and you'll be right back where you are now. Having the shop do it up front will avoid that. But no shop will do it for cheap if you bring in a wheel that you didn't buy there. But buy from them and they should do it for cheap or maybe no cost since it's a fairly quick thing to do on a new wheel.