There are a number of books, kits etc ava. I would also check local college ofering Horticulture clases. Check local greenhouses if they know of a company or individual doing this.

Googling for ~ propa "tissue culture" site:gardenweb.com I find a few dozen discussions on this forum.

Tissue culture is fun. I encourage you to venture into the area.

I think getting in touch with a local college/university/high school with a laminar flow hood and autoclave will be to your benefit. Sanitation is key and having the right tools will make this much easier. Yes it can all be done at home, but having access to appropriate equipment will save you time and heartbreak.

Bring me up to speed. What plants can best be propagated from tissue culture?

"...[b]est be propagated from tissue culture?"

There was a time when students almost always started with carrots as this was easy for educational purposes.

Professionals use tissue culture aka micropropagation anywhere they want to produce many propagules with the same genetics. It is a good method when one wants large scale in a small place and the plant does not produce seed echonomically.