Is there such a thing as affordable tile and grout? 

The short answer is yes, if you're willing to do all of the installation work yourself, and shop for bargains. You can purchase 12" x 12" tile from many home improvement stores and some tile shops for less than $0.49 a square foot, and sometimes cheaper than that when its on sale. Is it the most beautiful tile you've ever seen, probably not, but it is a solid surface material that will last for years and stand up to abuse a lot better than vinyl flooring, aka linoleum. Installing tile flooring is not out of reach for the homeowner with an average skill set. Floor tile for a laundry room with dimensions of 8' x 12' would require 96 square feet of tile, and would cost less than $50 for the tile. Head on over to a discount tile store near you, possibly a Floor and Decor, or a Home Depot or Lowe's and pick up 4 or 5 boxes of the cheapest floor tile material they have, 7-8 pieces of hardy board, 10 lbs of grout, some spacers, and a 50 lb bag of tile thin-set.

You can find many online videos showing how to install tile directly on plywood and linoleum. Of course you want to apply a backer board, or some sort of moisture barrier, but that will be up to you. By now you've invested less than $200 in materials for a new tile floor, and you have lots of work ahead of you. You can borrow a tile saw and float from your friends, and save money using their tools. Is it going to be easy? No. Will it look good, yes. So the bottom line is, yes, there is such a thing as Affordable Tile and Grout. This is an over simplification, but it is used to express a point about cheap tile floors.