Where can I find square boxes or barrels to plant greens, beets carrot

Lots of nurseries have them in our area

Boot Sales - or make them from old Pallets......

5 gallon buckets are frequently available for free from FF restaurants, etc. - ask them to save for you --- be sure to use drain holes in the bottom SIDES of the buckets, not the Bottom -- it will be sitting on the ground, and the excess water won't drain as well

also the option of the 'tote' used for storage -- seasonal ones in red/green are on sale here 18 gal for 3.99 --- any time you do container gardening you should use a good quality potting soil -- not 'yard' dirt --

Home Improvement stores should have inexpensive barrels and buckets.

Buy 18 quart totes.

Here are some good ideas for you

You could make your own from free pallets!