I'll second most of the advice here. Wonderboard is a really good idea if you have the vertical space for it, but if you're already 3/5" above the surrounding floor, another 1/2" of wonderboard isn't going to help things unless you can tear down a bit.
Tough to tell from your pic, but I wouldn't be suprised if there is another layer of flooring under the current linoleum. I'd be kind of suprised if it was asbestos, but worth checking before you start making dust.
Also, in my experience, a cheap score & snap cutter is easier, cheaper, and just as good for ceramic tile. You should only need a saw for stone.
Make sure you have the right kind of grout. If the tile has a glossy finish, you want unsanded grout, and will want to run thinner grout lines then if you have a more mate finish tile.
I sat through one of those DIY tile laying classes @ Home Depot, and the guy was actually pretty good. I learned alot. I've got a slate floor, and a ceramic tiled shower to my name right now, and about 200 ft^2 of marble out in the shop for if I ever get to finish my addition.