Depending on what you actually end up with for artwork, I'd either V-Carve with a 45° or 60° bit, or use a 1/32" or maybe 1/16" bit to pocket it.
As for finishing, I'd spray 2 coats of laquer, engrave, then paint, and sand on my 6x48 sander to remove excess paint, and laquer again. Although you probably need polyurethane or varnish for coasters.
I wouldn't buy the In-groove bit unless you're just cutting outlines.
And if you're buying models from Vector Art 3D, don't buy Cut3D. Use Vector Art's free CAM software, which is a version of Cut3D that only works with their models.