How Do You Tile The Ceramic Tile Floor?

It is really up to you as to whether you tile the whole floor or around the cabinets, but remember that if you tile all the floor, your cabinets are going to be somewhat higher. Is that going to affect your plumbing for the sink? I would put the cabinets in first, then lay the tile. This is just my preferance. It also saves money on tile, grout, and thinset. You have to make a few extra cuts, but that's no big deal if you have a good wet-saw. I would suggest you rent a good one instead of buying a cheap one, if you don't have access to a good one.
Just my opinion, but would definitely pull up the old linoleum because it could start to breakdown over time,"I have seen this happen", and then your tile would start popping up. Laying a tile floor is a lot of work, so you wouldn't be too happy if you had to do it all over again. You can purchase a scraper at the Home Depot , Lowes, etc., to scrape the linoleum up with.
You don't say what kind of subfloor you have under the linoleum. If it is concrete, you don't have to lay backerboard.
Just make sure you get your measurement right by finding the center of the room and starting your first four pieces of tile in each corner of where the center lines cross. + And make sure you use thinset mortor mix on the floor. Mastic is for walls and countertops.