You could drill the body and neck holes in one go, or you could drill the body holes first and then the neck ones, as the body holes will then act as a guide for the drill. But do clamp the body and neck together when drilling the neck holes.
As Robin says, use the neck plate as a guide. Look at pictures of other bolt-on neck joints to see where the neck plate fits in relation to the edges of the body.
I don't have a drill press, but I do have drill stand, which helps to keep the drill vertical.
There is also this sort of metal drill guide, which will also help keep the drill as vertical as possible and is useful for smaller items or where space is limited and a drill stand won't fit.
Both are useful tools.
The initial body and neck holes should be the same size, and the drill should be the diameter of the central solid part of the neck screws. Once you've drilled the neck holes, the body holes should be re-drilled out to the outer diameter of the neck screw threads, so the screw just fits in the hole without needing to be screwed in.
Here's a good video on why this should be done. Unfortunately, even big manufacturers rarely do this, but drilling out the body holes can give a much tighter neck join.
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