Or in this case, lay tile. I'm actually tiling my kitchen next week, and went through the same thoughts (tile the entire floor or around the cabinets.) I decided that I'm going to put down a new mud base and tile the entire kitchen. My though it this: My subfloor is out-of-wack to begin with. The mud will serve to level the floor and provide the best base for the tile. I'll put the cabinets on top of the tile, that way, should a future owner want to replace the cabinets (or me someday), I will be able to re-arrange the kitchen without replacing the tile floor.
As for removing the old flooring, it really comes down to spending lots of energy. There are some gle removel products on the market that work pretty well to clean off the residual glue, but you need to get down to the concrete first. Get a good floor scraper and get ready to work.
One more thing - make sure the subfloor is clean before you put down tile or it may not adhere well.