A couple of years ago, a member described his method of planting 2 or 3 seeds in each corner of 4" or 3.5" square pots, then culling/clipping weaker seedlings to just one in each corner.
I adopted/adapted the basic principles of this method, so that keeper tomato seedlings (in the first germination starter container) would stand almost 2" apart. Also in J. Jeevons book How to Grow More Vegetables..., he recommends 3" deep flat for starting most seeds. Obviously, smaller seeds can be closer together (maybe 9 in a 4" and larger seeds need to be farther apart). His book also describes the container depth for growing to transplant size depending on the plant.
Ideally, I like to use Jeevon's recommendation to cut apart the soil in the seed flat with a sharp knife (to clean cut the roots) like a sheet cake 1 week before uppotting, though I admit I don't always.
I use all kinds of recycled containers as well as square and round plastic pots. I found out last year that transplants uppotted into small clay pots performed the best, so I'm trying to increase my clay pot inventory, though they're heavier, not as space-saving, and harder to handle sometimes....