I'm going to attempt a comprehensive answer even though you don't say where you are--could be important--or what cover crop you have in mind.
I am in West Virginia, zone 6. I have two gardens with permanent beds, all of them 12 feet long and varying between 2 and 4 1/2 feet wide. I pooh pooh the "grow perennials" suggestion--there are few perennial vegetables (unless maybe you live in California--pretty mu ch all fruits are perennial, but that doesn't help with vegetables.
Here, onions come out about July 1st so it works to plant them around the edges of vine crops like summer squash or melons. But my carrots need at least another month and would be drowning under the vines. Actually, I plant my carrots in two beds in rows across the bed, alternating with onions--the onions go in in March, and are up marking the rows when I plant carrots in April. I once read this allows each to repel the fly that bothers the others--I don't know but it seemed I got better crops after I started doing this so I still do. But we eat a lot of onions so I also plant a solid bed of onions, and usually a few tucked into the corners of beds with slow crops. Sometimes I plant garlic in the fall in a grid pattern: a double row down the middle of the bed, then short rows across the bed, so that in the spring I can put tomatoes, peppers or sweet potatoes in the spaces between, and the garlic or onions come out just when the rampant crops needs the space.
I believe in crop rotation unless your garden is so tiny it makes no difference--but the permanent bed system makes it more meaningful. And I have three garden spaces a couple of hundred feet apart. This, by the way, is useful for two reasons--one is effective rotation of disease-prone crops (tomatoes and peppers for me, mainly, tho I have had problems with cercospora on chard and feathery mosaic disease on sweet potatoes. The only insect I have significant trouble with is the two kinds of worms on brassicas, which show up every year, repeatedly. The best solutions there are tulle fabric (netting) over the crop if you can find a frame work big enough, and Bt--bacillus thuringiensis, a naturally occurring bacteria that kills soft-bodied bugs. I have enough weeds, and I allow several wild, ornamental plants to grow in my garden--mullein, butterfly weed, yarrow--that the predator bugs and pollinators are content and effective.
One issue with cover crops is that they are mostly used over winter but you seem to be saying you'll grow them NOW. You also mentioned winterkilled crops; living roots in the soil all winter is better for the soil health, but a winterkilled type makes sense for a spot you pan to put an early crop, which wouldn't get any spring growth before you turn it under and plant. Daikon radishes are good to plant once in each area, because they drill down into the subsoil, then die around 15 or 20 degrees, leaving a bit of organic matter extending into the subsoil. Especially good for subsoil.
I mostly use hairy vetch and winter peas in my main gardens, because they're easy to rip out in spring. Rye and wheat do a better job of building biomass in the soil, but if you dig them out in spring, it's hassle to try to shake the dirt out of the roots, especially if you have clay soil like I do. However, if you wait until they're shedding pollen, about the start of June here, you can cut them and almost all will die and you can plant a couple weeks later. So I generally have a bed or two in one of those, with plans for a late crop--some kind of beans, or peanuts, a fast melon...to follow.
One of my gardens is left flat, and tilled once or twice a year. That's where I grow corn and sorghum. I try to get rye and vetch in there in fall, before the corn/sorghum is harvested so it gets a decent start--then I don't have to till in fall.
I've never used commercial fertilizer--my clay soil is often a pain to work with, but it's rich in nutrients, deficient only in sulfur. I try to put an inch of some organic matter everywhere every year--compost, leafmold, manure, maybe woodrot; and use mulch, mostly hay, almost everywhere.