You may also want to consider taking a tile setting class, usually free at Home Depot, and look into floor tiles that are slip-resistant. If your bath area is not large, then you ahve the advantage of considering higher-end flooring choices as the cost to needed amount is then really not prohibitive.
Link that explains the difference between vinyl and linoleum. This link also has links to other flooring info in the right frame:
http://floortalk.wfca.org/2008/04/02/linoleum-whats-the-difference-between-vinyl-and-linoleum-2/<snip>
Differences between Vinyl and Linoleum:
Vinyl will melt if a lighted match or cigarette lands on it, linoleum can’t.
Most vinyl patterns are printed into the surface, linoleum’s colors go all the way through.
Linoleum can be used on countertops and backsplashes where vinyl cannot.
Durability – linoleum can last 30-40 years where most vinyl cannot.
Vinyl was introduced in the 1800’s and vinyl flooring came around in 1947.
Linoleum requires an acrylic coating upon installation and then again annually where vinyl flooring does not.
Linoleum has more durable properties similar to those of ceramic and hardwood, but not the cost of those products. The cost is more similar to vinyl flooring which is not as durable.
The manufacturing of vinyl flooring uses highly sophisticated techniques, complex methods and precise systems, linoleum uses a more simple natural process.