having done a total home reno, and having front load washers, I can tell you the good news - and the bad news the good news is - that the type of floor is not particulary important the bad news is - the subfloor is critical - as the subfloor is what provides the support - and it is the hardest thing to re-inforce/change the subfloor on the main floor if you live in a temperate climate, with no basement or crawlspace, is likely concrete - which is generally extremely solid. otherwise the subfloor is likely wood joists with wood sheathing on top. When tile tile floors crack, the real problem is not what is ON the tile floors, but generally a weak subfloor beneath the tiles. The weak subfloor flexes with pressure on top of the floor. Tiles can not flex to match the subfloor's flexing - so the tiles break. The best solution is to put in newer, taller floor joists, but unless you are doing a total gut rennovation - that's practically impossible. The easiest solution - which may or may not be enough - is to put additional layers of plywood - one or two sheets of 3/4 inch thick plywood on top of the existing subfloor - and then cover with any floor covering you like. Another strategy, is to make sure that where your washing machine sits on the floor, is as close as possible to a support wall below. The joists will be stronger on their ends - which rest on a support wall/structure, than they will be in the middle. This may invlolve relocating some plumbing - but it is still much easier than adding taller floorjoists. If there is room in the ceiling/crawlspace below - you could add some supporting columns underneath the floor directly below the washing machine.

MY back is degenerated. We have Mannington stone look laminate installed over "hush step" pad which is about 1/4" thick. Ours cleans up with water, and nothing sticks to it so I don't have to spend a lot of time cleaning it. Nice on the feets and knees and back.

Since you have a basement underneath, and depending on whether accessibility from directly beneath the floor is easily accomplished, you may be able to additionally counter unforeseen issues through further reinforcing the floor. Your immediate concern appears to be floor covering versus the actual floor, and none of your selections actually add to the strength of the floor; very little, if any. Ceramic tile can crack it installed on an improper sub-base, synthetic tile yields a variety of very attractive choices, linoleum is an unsung hero of flooring for its durability. You did not mention the area you are covering? Just the laundry area, the kitchen, or both? Go with what pleases you best, and what you can live with for several years. Here is a good thread to better inform you about floor issues: Miele 4840 Vibration - Damaging homes?

It looks like reclaimed hickory to me...or perhaps chestnut? Old beams that have been turned into flooring. I don't think it's "yellow" enough for heart pine. Might have a wax finish on it...or waterlox tung oil.