Five gallon containers are good for many vegetables, including tomato, pepper and cucumber. I fill mine with commercial bagged compost, which works well. With a simple drip irrigation system, and using slow release fertilizer in the bags, the daily work with the plants is much reduced.
Instead of the more expensive plastic buckets, there are 5-gallon "tomato bags" available that only cost about $0.32 each. I found one source that will sell even a few, and not require an entire lot of 25 or more. They also sell the clips to attach the plants to the support string, again in small quantities. I usually wait until I need some drip irrigation parts as well to help lower the shipping cost percentage.

Finally, my small greenhouse floor is 3/4 in. crushed rock (8 inches deep). It drains well, does not grow weeds, and has kept the ground squirrels and gophers out.

Here is a link that might be useful: tomato bags

I'm curious why the rubber mats as a floor. I would think that weed block fabric would be cheaper, easier to use and allow better drainage.

Actually, the rubber mats are not a bad idea if there will be constant foot traffic. I meant to get pea gravel down in my greenhouse, but needed to do a little better leveling, so just put weed block down as a temporary fix so I could get on with the start of planting season last year. The first batch of more cloth like weed block started falling apart near the end of the summer. I have replaced it with some more plastic feeling stuff, but I'm sure that regular foot traffic down the middle of the green house will grind that to pieces as well. Got to get busy on that pea gravel!