Re: Is this a good starting set of mics for home studio?
Getting a pair of small diaphram condensers (SDC) allows you to do stereo miking. This applies to drum overheads, guitars, pianos, saxes, choirs, full and chamber orchestras, and literally all acoustic solo instruments and ensembles. SM81s are VERY good SDCs. They are staples in every major studio I've worked in since the 1970s. They are quiet, neutral, and versatile. If you have the money (because they are not cheap) get the two SM81s. You will not regret it.
The SM57 is another insanely versatile dynamic microphone. It is in every studios' arsenal. You can use it for snares, toms, kicks, guitar amps, and in a pinch even vocals. A must have.
I've not used SM52 Beta yet, so I don't know how it sounds. My only issue with it is since it is promoted as a specialized mic, it may not be versatile. My option would be to get another SM57 for your kick, or get an RE20 if you can afford it. The RE20 is another long time industry staple. It doubles as a fantastic vocal mic.