Here was my first attempt at gardening, jumping in blindly as you are doing. Needless to say it was a complete success and now consider myself to have a total green thumb. I would suggest reading up as much as you can on each variety, I would also suggest making a propagation/humidity chamber as your seeds will love you for it.
Cucumbers, carrots, tomatoes, cherry tomatoes and jalapenos were my first varieties. Everything went well except for the carrots, we had too much rain as you can see from the moss growing in there! That was a very wet season!
I have an actual greenhouse attached to my garage now so I have already bought most of my material for this next attempt. I'm aiming for a little more extravagant.