Considering a robot vacuum

I currently have a corded vacuum at home that I use about once a week. It works alright, though it would be great if I did not have to use it :) And then there is mopping. That's what I hate most, but unfortunately a lot of the dirt doesn't get vacuumed, and only goes off if I wet-clean the floor.

I have about 70sqm (750sqft) of white tiled floor. I also have to dedust things above the floor, but I guess no robot vacuum can do that for me.

My requirements are:

• The robot can clean the floor well (not just dedust it, but wet clean it properly).
• It can work around items on the floor (let's say a sock fell from the clothhanger, or a receipt fell off the table. I don't want the robot or the item to get damaged)
• The robot can work for as long as possible without my intervention. I know that eventually I have to refill the water, replace a part, or clear the bin, but I'd want it to do as many rounds as possible before I have to.
• I need to be able to make it not roll into my wet shower and die. If it can clean my shower without dying, that's great. If not, I want it to not go in.
• I don't have any pets or long hair.
• The floor-plan it a bit messy due to the way my furniture is laid out.

I am ok with any reasonable price, as long as the robot delivers. Are robot vacuums the right thing for me, or is their mopping game not good enough yet? What's the best option for me?