Okay, lots of ground to cover and I hope others chime in so you will have a variety of opinions.
1) Okay, in my opinion, the Handibot will be one of the safest power tools in your shop. That is not to say things can't go wrong, just that they will go wrong slower than on say a table saw.
A couple of thoughts here, always make sure the bit is correctly installed in the collet, the right depth and not too tight or loose.
Check files produced by students carefully, taking too big of bites will get you in trouble, wait, being too conservative isn't good either. You have to develop a feel for it and record settings for it the way I'm sure you do for your lasers.
2) Jigs and levers. I'm a big man but don't have near the muscle mass I once did as I march into geriatrics, two-person lift put it on a jig that has a hinge or where you can slide material under it. There's lots of prior art for this. If you have a specific use case and can't find anything, give a holler, and maybe we can find it together.
3)Depends on the look you are going for, but you got Vcarve with your handibot so a good bit to work with is a V bit. A 1/4" ball works well for mono-line fonts.
4) For the most part, you want to avoid most bits made for plane routers as they won't typically have the up cut or down cut spiral. Stay away entirely from bits with a guide installed.
My most used bit is a single flute 1/4" up-cut. These work great for cutting out sheet goods. For carving things from solid wood, you will want carving bits.