Porcelain tiles offer the best look, resale value, and strength for traffic. I just did my kitchen with them, and I have done my shower walls too.
Before you start SCREW down your plywood floor again to the joists below, should be easy to figure where they are underneith. Start at the edge of the plywood, screw where you see nails should be 16" centers along the length of the ply.
Screw every 6" along the joists with 1 3/4 screws.
If you want to have a water tight seal you need to use a rubber membrain, its orange with a honey comb style look. But its expensive, Ive always gone with silicone around the outer perimeter of the floor. If your not going with rubber, then you need 2 layers of plywood, the second makes for a solid base for tiles, If you dont the floor may still move a bit under the tiles and they will come off. I usually put down 1/2" ply, you can go bigger but it will really offset the height where your bath floor meets your hallway. The second layer must also be off center of the first, so your second layer joins must be at least 2' from any of the first layers joins and must fall on the joist as well, screw every 6" with 2 1/2" screws on the joists.
Cutting tiles can be done with a wet tile saw or a diamond tipped grinder blade. Both are noisy and messy, the grinder blades cost less (around $25) where the tile saw is likey a one time use for you and runs around $80 and up.
Use Mega Lite mortar, not Flex Rock, Im having issues with it. Bigger tiles need a 1/4"to 1/2" groove trowel to put down. I find that homedepot or any store like that has good deals on tile.
Stick on tiles are hidious to look at, have no resale value, and are cheap crap.
If you want use vinyl or linoleum, you still need two layers of ply, but the second is 1/4" smooth or good one side. Still screw the hell out of those joists, nobody likea a moving squeaking floor.
Homedepot has rolls of remenants for like $25 its usually 8'x6' or 8'x 12' cheap stuff, pick a roll you dont hate and you have a new floor. End of the roll might have more selection but you will still be paying $1.50 / sq foot atleast for it.
The glue isnt expensive but dont wear anything you like when you put it down cuz its going to get on everything. Ask for a trowel to spread it with.
Hope some of that helps.