All I want to do is tile the floor,
Do that last thing. You'll need some type of tile-backer.
With tile surround?
You could install the vanity before the tile and save a few dollars.
fixrite is correct.
Typically toilets are a standard 12" (to the center of the drain hole) from the back wall (but not always) so verify that dimension before you go to buy a new one.
Depending on what type of supply line you have you may need to buy a new supply line but that's not an issue at all.
I will be removing the old linoleum flooring in there right now as well
The old linoleum may have a 1/4" plywood underlayment under it that was installed when the linoleum was new. Remove that also. It isn't compatible with a tile installation.