R.K.
I use the swiffer wet jet, but instead of their solution, I use a spray bottle with Shaklee's all purpose cleaner. It's green, inexpensive (around $12 for a 16oz bottle of concentrate, I think, and mine has lasted 2 years), and it's safe around children and pets. I really love it.
www.shaklee.net/rkklemm
I also have something similar to a shark that is just a steam cleaner and uses only water, no chemical at all.
either way should work great, but my husband is the only one who has used the shark like thing we have. I find it to be a hassle to deal with the water. With the Shaklee cleaner, I just take my spray bottle, spray some cleaner on the floor, and then use the swiffer mop (I'm sure any kind of mop would work, but I already had the swiffer one and like how it works) to wipe it up.