They all act differently as seedlings and benefit from different treatment. I have not grown all of these, but tomatoes you will want to pot up when they get tall and you bury the stem deep. Do not do this with the other plants, just tomatoes. Pepper seedling I grow in those little peat pots and I plant them in their final spot when they have a couple sets of true leaves.

Most things benefit from being potted up after the first true leaves emerge...

EG

Here is a link that might be useful: My square foot gardening blog

I'm always a late bloomer when it comes to potting things up.

Usually I'll start in small black plastic 6-packs or something. Then when I start to see the roots come out of the bottom, I'll put them in larger containers - such as 16-ounce cups.

After putting them in the 16-ounce cups, they usually make it all the way out to transplanting.

I just planted a lot of broccoli, tomatoes, cauliflower, and peppers - and I put them in 16-ounce cups or larger - that way I don't have to worry about potting them up. But when I first started - with celery for example - I start them in those black plastic things and move them to the 16-ounce cups.

Regarding transplanting - I usually always transplant them at the same soil level that they were previously in. I would think that if you put them in deeper, it may cause the stem to rot.

Here is a link that might be useful: My Garden Blog