The size of the container really isn't that important. What is important is ample water and nutrients and the smaller the container the more frequently you have to add both.

If you are growing full sized plants MOST people will use 5 gallon buckets and larger for each plant. Some use 15+ gallon self watering containers and have 2 plants in them.

Yes, these are quite heavy to move.

You could invest in an Earthbox. They are about $35 but you can get them with castors so they are easily moved.

Depth not as important as volume.
Whiskey barrel or equivalent size for regular sized, indeterminate plants.
Anything smaller:
Dries out too fast=cracked fruit, blossom end rot;
Becomes top heavy and blows over in a breeze;
Becomes too root bound=can't take up nutrients as efficiently no matter how much you fertilize.
I am used to plants in the ground reaching 5 to 7 feet tall, so big pots are more likely to allow similar results.

If you grow determinate varieties or "patio" types you can use a smaller pot. Heck there are some varieties that only get about 6 to 12 inches tall so would do well in a 6 inch or 8 inch pot.

Earthboxes did not work particularly well for me last year (my first using them). I will try different varieties this year.

Think I'm going to try some 3 gallon buckets. Do these need to punctured in the bottom to allow excess water to escape? And what kind of fertilizers will be best for this sort of set up?

Thanks!

Drainage holes are always a good idea. Don't want the babies drowned every time it rains.
I like tomato tone-mostly organic so you need to apply frequently.
Non-organic fertilizer-Osmocote for veggies.

With 3 gallon bucket be sure to grow a patio type so it won't outgrow the bucket.

francescod...would a Roma be considered that? My goal is to do a ton of Roma's this year.

meta

I suggest you amble over to the Container Gardening forum to get the best information. There are some real experts there who have valuable information that you'll need to grow things in containers. The soil you use and understanding how drainage must allow air to infuse the soil are critical to success. If you understand the effect of both on your plants, you'll have a better chance of growing healthy and productive ones.

I've learned a LOT from them, and that always makes a person feel more confident!

Here is a link that might be useful: Container Gardening

No, a 3 gallon container is not large enough to grow a Roma plant, even a 5 gallon, while possible, would be pushing your luck. 8-10 would be much better.

Varieties are sized specifically - patio, bush, determinate, indeterminate, etc. There are both indeterminate and determinate varieties of Roma. Even the determinate variety of Roma is 4-5 feet tall and needs some stakes or other support. So with only a 3 gallon container plus the need to move them you need to stick with patio sized varieties.

I agree with Anney, your question is best answered on the Container Gardening forum.

Good luck.

Dave

PS: and by all means there MUST be drainage holes.