Your budget restraints are going to be the biggest problem...perhaps look for a porcelain tile that looks like granite or terrazzo...both will go with the mid-century vibe and show less soil and smudges

With your kids and dogs and budget I would not change it. We had the same flooring in a new house that we bought in1990 and kept it for 14 years before we changed it. btw our tile guy laid new tile on top of the old, but we were renovating the entire area which made that work.

Have you considered linoleum? It is made from linseed.

Replacing the tile is going to be a huge expense. You don't say what the space will be used for. Is that the living room area? Dining? It will be a lot more affordable for you to get different but complementary beautiful area rugs to anchor each space. Consider getting a good looking, durable runner for the hall. I wonder if your medium gray provides too much contrast with the white floor. Also the tile seems to have some brown in it, so the gray isn't doing it any favors. It's hard to offer advice since you're not showing us current room. You'd be better off with white or creamy tan walls then having art work, furniture materials pull the eye upward.

The tile is the cheap part. The labor will easily be 15-20K from a decent licensed contractor who isn't a side of the road bubba pickup. And who does the job properly and safely. And quickly.

Or else get that substantial upper body workout every night for a month with safety goggles and a sledge hammer, then a concrete grinders. Don't forget the dumpster and to be sure you're up on your tetanus and know the quickest route to the emergency room.

Really, there are bubbas which can be picked up by the side of the road? That sounds like potential trouble. Bubbas should only be picked up in well-lit safe places such as police station lobbies.

BTW there are laminates made that do not have formaldahye

Check out Floor & Decor, if there's one reasonably close to you (shipping can be a killer) -- they have a couple of nice large-format concrete-look gray tiles that are pretty great and in the $1.75-2.25 price range. I think that's likely to be a better choice with your house than wood tile.

Laminate floor might be your best choice as it can likely be installed directly over your tile which will save on demo. However, if you expect to have no issues with the laminate, you have to avoid the cheaper varieties.

Wow, thanks for all the helpful responses!

- Linoleum: I didn't even know they made that anymore! I assumed vinyl replaced it. I remember this from my grandparents' homes- it's so durable! A quick google search suggested it is out of my price range for now but perhaps it would be worth it to wait another 6 months to a year.

- Laminate: I did not know that there was formaldehyde-free laminate available. Thanks for the tip!

- Tile: Thanks for the tile ideas. Thankfully, labor will be at no cost. This is our first home and as a housewarming present, my stepfather (a licensed contractor) has offered to take the old tile out and install new flooring- as soon as we can afford and choose!

- Floor and Decor: I looked it up and found one about 30 minutes away, thanks!

And to answer the other question, the tile runs from the living room, into a dining room, kitchen, bathroom and hallway. It is also underneath the carpet in a bedroom. The room in the photo is the living room. The tiles are actually all white, but they are so dirty and stained from decades of wear. We had them professionally cleaned but they still look gross.

I appreciate all the help from everyone who answered! You guys had some great ideas :)

I would go with a darker porcelain tile in three different sizes in a slate look laid in a versailles pattern. The upkeep is low and quality very high.

Your new tile will not be as expensive since your step father is doing the work himself. Whenever we have had floor tile issues, my husband has removed the old tile and replaced it with new and the only expense is the tile, grout, and whatever else he has needed to finish the job!