OP: If you don't know how to ascertain which wheels are compatible with your drivetrain, I think you should go to a shop (ideally the shop at which you purchased the bike) for help with choosing a new wheelset.
And even though you don't want to hear it, you will be spending money in an attempt to turn a sow's ear into a silk purse. Rather than upgrading a bunch of parts, you'd be better off (economically) by just buying a better bike and relegating your old one to the trainer or for rainy day riding.