It's not quite as complicated as you may be thinking
First question (which may be a non-question if your coop is already built) is: raised wooden floor, or on the ground (dirt or slab). If there is ANY tendency for the site to flood WHATSOEVER at any time, raised wooden floor is the way to go. Otherwise, your choice, they each have their pros and cons.
Second question is what material to use as bedding. If you have a raised wooden floor it is generally best to stick with drier materials/methods -- you CAN have damp stuff on a raised wooden floor but it won't last so well. Shavings are really easy to clean, but some people prefer other materials (especially if they are available free to you). EXPERIMENT, try different things, see what you end up liking, use that
Third question is how to manage it -- deep or shallow litter, clean frequently or infrequently or almost-never-except-spot-cleaning. Again, I would suggest you EXPERIMENT, try different ways, see what works for you, then do more of it
Note that there is no "the" deep litter method, there are a whole buncha different ways of managing deep litter, some BUT BY NO MEANS ALL of which involve damp composting in the coop, and those damp-composting-in-the-coop methods do not work NEARLY as universally or straightforwardly as a lot of happy webpages etc would have you believe. THey are appropriate for some situations but not appropriate for others. Don't have preconceptions -- just mess around and see what ends up working best for you.
serious rat problems. <snip> lay cement pavers from home depot to make a base, site the coop and run structure on it, then use wood shavings on the pavers. (The girls will have a separate larger run adjacent to the all-in-one structure.) He told me this would prevent rats from tunnelling into the coop and the runs would be easy to clean. He said this is a good alternative to running hardware cloth vertically in an underground barrier around the coop. Thoughts?
Yes. Good plan. That is the best you're going to get, short of a solid slab. You need to set those pavers very, very correctly/flat/tight, but yes, it will work reasonably well (i.e. you should still keep an eye out, as they can chew thru wood or actually lift pavers). It will actually work far far BETTER THAN burying hardwarecloth vertically, which rats will just cheerfully tunnel under. Make sure you do a superb job laying the pavers. Use the largest pavers you can get -- 18x24" is good, tho a nuisance to carry -- as they are more ratproof (they can't tip 'em up as well)
Good luck, have fun,
Pat