An inexpensive laminate flooring can be a good choice.

Forget the laminate..You can't ever hot water mop them...out of the question in your case...A loose lay fiber floor is what you want. Tarkett makes some inexpensive ones and also Airstep Plus from Congoleum. The fiber floor can go over top of your tiles and will suck down tight. you will swear it is glued down. It is definitely what you want and will not set you back a fortune. Laminates cant be mopped ever..just damp mopped..very little water. Good Luck

I would go with the laminate - It won't hold up well to mopping, but it should hold up good enough for the time you intend it to be there. It has to be the easiest flooring to put down and take back up.

We used that as a temporary floor in our kitchen. Did not really mean to at the time, but plans changed and it didn't hold up as well as we hoped. After a year we knew it was going to be replaced so I didn't worry about it after that- and when we took it out three years later it had handled the job of temporary floor just fine. We got the stuff on closeout so weren't out much $$.

We now have ceramic tile - and had to beef up the subfloor after we pulled the laminate up, but that had nothing to do with the laminate.

Here is our "temporary floor" This took a day to install.

Here is the final floor - put this in last winter.

One advantage of laminate - you can lay half the floor and move everything on top of it, and then lay the second half. Of all the flooring I've installed, click fit laminate was by far the easiest.

I'm not familiar with some of the new loose lay flooring. I've laid some perimeter glue vinyl, and that was way more work in cutting and fitting than laminate, though not as much work as full glue down vinyl.

Mopping it with hot water and Mr clean could ruin an inexpensive laminate in a matter of weeks. I will not argue with posters here as they are entitled to their opinions. I do not care what others do. I will say I asked the president of my company a couple of days ago your exact question referring to you...his answer was fiber floor which actually surprised me as to his solution was exactly the same. 1st of all if your temporary floor goes longer than 18 months, which many times it does....a Fiber floor will hang right in their for many years...mop it, spill water on it, your pets can pee on it, it just wont matter. You wet mop a laminate floor two times and it will begin swelling at the joints...That's just a fact. And a fiber floor can be laid in about a tenth of the time a laminate floor can be installed. Those are the facts...and I sell 1/4 million feet of laminate annually compared to 70,000 sq ft of vinyl so it isn't like I am anti laminate. But ultimately, it is up to you. Water and Laminate mix about as well as water and oil....They don't..

Here was my experience in my old cottage at MoccasinLanding.
I got a sheet vinyl and laid it over the existing asphalt 9" squares original to the house. Around the rim, I had the quarter round put down. It worked VERY well, even with 2 dogs 2 cats and 16 parrots. Parrots make a lot of messes, and it was very easy to clean the vinyl sheet. When I sold the house about 2 years later, the same sheet vinyl was down, and the new owners took out everything afterward, but it still looked shiny, even with all the constant cleaning. The product was cheap, easy to put down, cleaned like a dream, and lasted as long as I needed it to.

Now in this house we are doing the same sort of thing you are doing. We had the worst looking worn out damaged sheet vinyl you ever saw on the kitchen floor. The back porch also needed to have some flooring installed since we were planning to use it as it existed for a couple of years until we could unify the two spaces with a remodel. So I made a choice of 16" square sticky back vinyl tiles from Lowes (a mottled terra cotta color) and it is NOT a shinyy surface. DH installed it all himself, and it is quite nice and wears well. We now have only two dogs and two parrots, no cats, and the wear and tear is not as significant. But the product has been down about a year and looks as new as when we installed it. When the time comes we will remove all the layers of asphalt tile and vinyl tile down to the subfloor and lay new wood foundation for the porcelain tile we have already picked out. BTW, the sticky back tile has not come loose, and it is easy to clean. No shine on this product.

And this picture shows how he repaired the rotted floor after we removed the old gas waterheater, and then finished laying the sticky back vinyl on the back porch.