I think a little more info on what your gym DOES have would be helpful
Is dumbells + bench all you have to work with ?
Does it have any other equipment
eg. leg-press, pulldown machine, or any others - dipping/chinning station ?
Knowing this people may be able to advise you better on what exercises to do.
How to train depends on your goals - to make the most of your time I would do a routine that emphasizes low volume/high intensity of effort, but not neccessarily to failure. ie after a brief warm up move quickly to using meaningful poundages (>70% of 1RM) and do 1-2 really hard working sets.
If you want to avoid training legs too often then:
Mon: Upper body
Wed: Lower Body
Fri: Upper Body