The first year you should not need fertilizer for almost anything as you've got more than enough nutrients in the compost. That said, I did use a 5-10-10 general veggie/tomato fertilizer for my SWC tomatoes... and I'll supplement with nitrogen for my corn after they've grown a bit. Other than that, I haven't fertilized and my plants are growing fine. Oh, I also used a bit on my blueberries to increase the acidity and promote growth.

When I replant, I will mix in a bit more straight compost (my own this time) into the top to provide the nutrients for the next crop.

When my brother's dirt got old, he planted a cover crop that he tilled in to provide natural nutrients.

There are plenty of good alternatives to fertilizers, but thatever you want to do is fine.

Here is a link that might be useful: Sinfonian's garden adventure!

I would recommend adding some composted manure or just plain compost and a handful of some good organic fertilizer as you are replanting each square. The organic stuff will cost more but will not burn because it breaks down slower and has many trace elements that will insure plant health and productivity. Since it breaks down slower, soil vitality will improve over time.