Aha! You've come to the right place.
First of all, welcome to the HG!
Feel free to stick around the show us pictures of your boxes and your plants as they grow. And offer any advice that you may have.
Synthetic fertilzers are actually not that great. I used to use them as well. But, what they do is feed the plants and not the soil. They end up killing beneficial soil microbes that help your plants. Furthermore, you run the risk of burning your plants with synthetics. Instead add a handfull of kelp or blood meal to the each whole when you plant your seeds or plants. And fertilze once a week with a liquid seaweed or liquid fish fertilizer.
Add some compost for your humus and add some manure as well. It will help your plants.
Tomatoes and Squash are companion plants so that's good. With regard to growing your tomatoes, use a cedar stake to tie them to and old nylons work great. Don't use gardening tape because it stretches. Sucker your plants each week to increase your fruit production.
How to do this?
Between the apex of the main branches and the stem, you will see little leaflets growing; pinch these off.
When planting your tomatoe seedlings; pinch off all the branches except for those of the crown (top leaves and branches) and bury the entire stem in the ground. Add a handful of kelp meal into the hole and bury. Water thoroughly.
Squash will go slow for the first bit and then it can really get away from you. So just beware that it can take up a lot of space but, this is a good thing because it will shade the soil, and help smother out weeds.
Try planting beans as well that will climb up your tomatoe vines and feed the tomatoes as well.
Have fun! I'm sure everyone else will soon be offering you their advice as well.
Remember ask ten different gardener's the same question, get ten different answers!