This is for vegetables like tomatoes, peppers, eggplants and squash

Pot size is immaterial for sprouting seeds. There is no best size.

Even if they would stay in the pots for months till they can go outside? I don't want to start them in small pots and then move to bigger ones as they grow.

The problem with large pots is it's hard to keep them uniformly wet to allow the seeds to sprout without drying out/rotting.

I don't think I need such a large one. I have to measure the ones I have at home. I think they are 1/2-1 gallon pots.

I think it depends on the plant. Like fo tomatoes and peppers, I start in 1" Square cells. I pot up from there. For squash and beans, I use 3" pots to start with. I use a lot of red solo cups too.

I use 3 oz. bathroom cups. With a hole drilled in the bottom of them.