Try WD-40 and 0000 steel wool on the rust.
As for checking, just make sure everything turns freely by hand. The chuck won't spin like a skateboard wheel, of course, but make sure you don't hear any grindy noises, that's no "tight" spots, etc. Try and set it so that nothing but the spindle turns- there should be levers to disengage the gearbox.
Then make sure there's nothing in the chuck that might get flung out when started.
After that, plug it in and hit the switch.
You'll want to look for lube points too- the headstock should have sealed bearings, but there will likely be spots on the leadscrew, tables, handwheel mounts, and so forth, that will need to be lubed.
And, it should be said, keep in mind that's a 3-in-1 machine; generally speaking they're built cheap, and kind of inherently not all that rigid. Don't expect too much of it.
Doc.