Growing Carrots & Plant Suggestions for our Garden?

Today we went out and bought some additional plant starts for our garden. This is only our second year :) so we have yet to start our own from seeds. I saw no carrot starts. I was wondering if carrots are always brought up from seeds or perhaps it is too early in the season for carrot starts? What’s up??

Also we have the following plants for our garden and still quite a bit of space. What additional plants would you recommend (it is a vegetable garden)?
Bell Peppers (2 kinds), Tomatoes (3 kinds), Broccoli, Zucchini, Onion, Lemon cucumber, Mint, and Oregano. (It is too small a space for any large melons or squashes).

I apologize in advance if these are silly questions but like I said this is only our second year and we are going at it alone without any gardening mentorship. BTW the first year turned out fantastic.