If you want two displays natively through a single port, you should be looking for Thunderbolt.
The M1 Pro only supports two monitors natively, regardless of how they’re connected.
For two monitors, yes, you could plug one into a USB-C hub and the other into the HDMI port. Or you could plug them both into a Thunderbolt hub/dock like this (which would support 2 x 4K @ 60Hz). That is probably one of the cheapest options, but there are more expensive ones out there if you’re looking for additional connectivity.
If you want to charge your Mac, you can either get a hub/dock with pass-through power (to plug in your Apple-provided power adapter) or a dedicated AC adapter. With that said, I haven’t seen any Thunderbolt hubs/docks with pass-through power.
Some options for Thunderbolt 4 docks that would support multiple monitors are the CalDigit TS4 and OWC Thunderbolt Dock.
But … you mentioned that you didn’t want to spend $300, so IMO you could either go for the $150 mini dock or commit to plugging one monitor into a hub/dock and the other into the HDMI port on the Mac.
Finally, there is the DisplayLink option. I believe with something like this you should be able to run two monitors through that and one through the HDMI port on the Mac, but with some serious limitations (e.g., you will have to disconnect the adapter if you want to watch Netflix).
https://www.amazon.com/dp/B09RMVL865
A little late to this post but easily the best option out there IMO