Above is a good general answer, but your list
corn, beans, tomatoes, carrots, lettuce, onions, asparagus and potatoes
is kind of a mixture of stuff.
The lettuce, carrots, and onions are cool weather stuff. If you can plant your peas, you can plant the lettuce carrots and onions, directly in the ground. Mine have sprouted already and we had frost last night again. Onions in fact do well planted in the fall and over wintering.
The asparagus is a perennial. It's rarely started from seed. Usually people buy crowns (roots) of year old or so plants. They are cheap to buy. Planting crowns, it is three years before you can eat (much) asparagus. Starting from seed adds a year to that. If you are going to start them from seed, I'd start them indoors, now. Soak the seeds in water for a couple hours first and then they take about 3 weeks to germinate.
The tomatoes I start indoors 8 wks ahead of the average (50%) last frost date. But note the 50% in there. That means based on 100+ years of historical data, 50% of the years there is no frost after X date. But in these global warming times, generally it is less than 50% of the time there is no frost after that date. Sometimes if you look for last frost date you will find the 90% last frost date. If you have something very tender and expensive or irreplaceable use that one, but otherwise it is excessively conservative and will slow your garden down.
Corn and beans are usually direct seeded in the ground once the soil has warmed up.
Potatoes are usually grown from "sets," that it cut pieces of potato with a sprouted eye.