you are still talking in big generalities (vegetables covers a lot of territory) so all I can do is give a few general tips.
There are two main categories to be aware of in starting seeds:
warm season vs cold season
direct seed in the ground vs start ahead to transplant
cold season crops are cold hardy, often even frost tolerant, but often don't like hot weather too much. They include all the green leafies (lettuce, spinach, swiss chard, kale etc), all the root crops (carrots, potatoes, turnips, beets, etc), all the brassicas (cabbage, broccoli, cauliflower). They all want to be planted early.
warm season crops are pretty much everything else -- tomatoes, peppers, squash, beans, corn etc. They don't want to go in the ground until the soil has warmed up. Squash and melons are the warmest of warm season crops, tomatoes, beans, corn a little earlier.
Direct seed in the ground is things that are quick germinating and quick growing like peas, beans, squash or things that don't like to be disturbed once started, like carrots and other root crops
Start ahead are the things that are slow growing and need a head start if they are going to produce in a season. The shorter your growing season, the more things it will pay to start ahead. Tomatoes and peppers are the classic ones, but winter squash, pumpkins, brassicas, etc.
So if you combine the categories, you get:
direct seed early, as soon as the ground can be worked (i.e. it is unfrozen and dried out enough to be crumbly): lettuce, spinach, chard and other greens, peas, carrots, beets.
start ahead early-ish (I don't know your climate well enough to know when this is, but a couple months ahead of your last frost date) tomatoes peppers. I usually start the broccoli very early (like NOW) because it is a slower growing cool weather crop.
Direct seed once all danger of frost has past - beans and corn
Direct seed once soil has warmed up - summer squash, melons
Your seed packets should tell you things like "can be started indoors 6 -8 weeks before last frost date" (or 8 - 10 weeks or whatever)
Hope this gives you some ideas. If you look around on line you should be able to find some planting guides for your area that give more specifics.