Here's a vegetable planting guide put out by LSU:
https://www.lsuagcenter.com/NR/rdonlyres ... IGHRES.pdf
but like any of these, you have to take with a grain of salt and develop your own experience.
I looked at it and it says plant tomato seed starting 1/1 and pepper seed starting 1/15. That doesn't make any sense to me since peppers are slower germinating and considerably slower growing than tomatoes. I would reverse it.
The melons will need to wait for awhile. Tomatoes can go in the ground as soon as danger of frost is past. They are actually pretty cold tolerant once hardened off. The peppers can go out very shortly after. But the melons need the soil actually warmed up and they are very fast growing. Some people just put them directly in the ground once the soil is warmed up. I still start things like melons and squash indoors, but not until my average last frost date.
The other way you can figure this stuff is to find out when your average last frost date is and count back from there. Pepper seeds would be planted 10 -12 weeks ahead of last frost date, tomatoes 8-10 weeks ahead, melons 0-2 weeks ahead.
But along with the dates, what is important is the conditions you have for starting your seeds. "Way too spindly" sounds like they were not getting enough light. It does not work just to put your seedlings in front of a window, you will need to provide supplemental light, like fluorescent tubes set just a couple inches above them, on 16 hrs a day.