The first and foremost aspect to consider when starting your home machine store is whether this is for business or pleasure. If you just like to tinker and revel in fixing things yourself, you can get by with much smaller, more flexible machines than if you're going to accept outside work.
There are basic machine shops which perform the majority of the jobs you will encounter, the drill press, the milling machine, as well as the lathe. The house hobbyist can usually get by with a multi-purpose machine which incorporates all three of them into one versatile machine, but the severe machinist might want to set up shop with individual machines.
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The next thing to consider is floor area. You can purchase bench top drill presses, benchtop mills, and bench top lathes at very affordable rates, so even the home hobbyist may wish to consider this avenue as opposed to the multi-machine.
This allows much greater flexibility and will help to eliminate the set-ups and tear-downs you will probably encounter in case you just have the multi-machine. There's nothing more frustrating than having to tear down a milling job merely to drill a hole to be able to produce a special clamp for the exact same milling job. For your home machine shop, you'll have to acquire much bigger equipment.
You may have the ability to eliminate one of those bigger benchtop mills when starting out, but I would strongly advise that you get a large drill press using a #4 Morse taper spindle and as low an RPM as you can locate.