I like GunLine cutters for laying out the work. They're more aggressive cutting and you can (carefully) sharpen them. The coarse teeth don't load up as fast as the fine file-like teeth of the finishing type tools, though those get the call for the final pass to clean things up.
I've used both DemBart & GunLine finishing tools in the past (fine cut) and find them about the same.
IIRC one mfg'rs cutters can fit onto the others handles but not the other way around. I forget which.
Carbide single point tools are available but they are much more expensive than the carbon steel type. The advantage is the tool life. You'll realize that when the regular cutters dull w/o even finishing up one decent size job.
Even quicker when recutting old work with the grit and grime packed into the checkering. I've got some carbide single point cutters that are 25+yrs old and are still going along.
I'd suggest both a long and short single line cutter. The short tool is going to be needed to get into the corners of the pattern(s) when the lines are very short.
Trying to make do with the longer tool will usually result in slips outside of the border done with the heel of the tool while you're watching the point cut.
You may want a veiner chisel for getting into the impossible areas that a checkering cutter won't fit. They're also great for the tightly curved borders. Can be kind of tough to learn to sharpen at first but once you get the hang of it, it's a very handy tool.
A couple of spacing tools, right and left hand in what ever LPI you're going to work in.
..rhmc24's suggestion about getting handles for each cutter is wise. Changing them is not something you want to be doing in the middle of a project.
Do yourself a favor and use at least some gentle magnification. Even 2X will help alot.
A light that you can move around to give yourself a shadow of sorts accross the work will show the lines better than a bright light shining directly on it.
If you like the work, you'll end up with cigar boxes full of extra cutters,, checkering handles, patterns, and even a Foredom/MMC electric checkering machine w/extra handpieces to speed the work.