Good kit is the answer.
Shure SM58 are the standard to go for (about 100 USD). You cant plug these into a guitar amp without it sounding horrendous (Low Z output from a mic, not line / guitar level) which means some type of dedicated mic amplification is required. Fender do a Passport PA system which is probably a good place to start. As for cheep / hi impedance mics, Im with kimbob, they will give you nothing but grief !!!! Unfortunately this is one of those problems that is made a lot better by throwing cash at it.
As for monitors, well when you are practicing, if you are using a sort of PA thing, you can always turn the speakers to face you and adjust the volume / gain so that they don’t feed back (your mics will be pointing away from the speakers which should help also !).
Best of luck Dude
S