With non-tubeless rims you will have to run some kind of Stans setup with a rimstrip and latex sealant. You have the option of any kind of tire keeping in mind Tubeless Specific tires will have stronger sidewalls.

I run XTR Tubeless wheels and Maxxis UST tires. With a tubeless rim and tubeless tires you have the best protection against flats because they are designed to be run without tubes. If you are going to turn tube rims into tubeless, you might want to do some research at your local bike shop on options to convert wheels in this manner. I think the biggest issue is without tubeless tires you will have to use a compressor to encourage the tire to seat and even with a compressor, some will always leak.

I am not that well versed on tubeless conversions so I would ask at your LBS.

Good luck!