OK I'd suggest, if at all possible, to get someone to plow it under first, then rototill it but if that isn't possible just rototill the heck out of it--tossing the sod shouldn't be necessary and will cost you nutrients, just till it in good and most will decompose over the winter. The first couple of years you'll have a few weed problems but if you keep at it you'll get them out--half the enjoyment of a garden is getting out in the sunshine and getting your hands in the dirt. Given that it is fall and you live in Ontario, I'd take the 2-yr old as well as any new chicken bedding and rototill that in good as well. By spring it will be composted enough to enrich the soil and help the plants. BTW, I'm a great believer in using black plastic sheeting to mulch the garden--it warms the soil, keeps the weeds down and holds moisture. I even cut holes in it and plant my potatoes in them so I don't need to hill or weed them.
As far as the choice of plants.
Asparagus needs a couple of years to become productive. It does not do well in weedy areas so I'd suggest giving your garden a year of weeding before planting the roots. Mulch the bed well once they have come up--wood chips are best. It will then take about 3 years before you dare harvest any, 4 to 5 before it is really going to be productive.
As far as
beans are concerned, I prefer bush but have friends that go for pole beans since they take up less room. Pole beans do, as a rule, take longer to produce but produce over a longer period--I take care of this by make successive plantings. I would suggest adding nitrogen-fixing bacteria inoculant this first year since you're planting were beans haven't been planted before. Once the bacteria are in the soil there is not need to do it again.
Beets and
carrots are fairly easy and can be planted early. Unless you have really deep soil, I suggest "half-long" carrots. The last few years I have been using "pelleted" seed for both carrots and lettuce--this allows better spacing of the small seeds. There is a drawback, however, there has to be a lot of moisture present so the clay coating dissolves or the seeds don't germinate. Keep in mind that beet seed contains multiple seeds so there is no way to space them, they will have to be thinned once they get up fairly well. On the other hand the thinned out seedlings are excellent greens, both cooked and in salads.
Garlic is best planted in the fall--I'm about to plant mine if Burpee gets the bulbs to me and the garden dries enough to rototill. The bulbs start in the fall then grow through the spring and summer. They are harvested in late summer.
Onions can be grown from sets or plants put in in the spring. You probably live too far North to consider seeding them in unless you're going to start them inside first. I generally buy plants but they come in fairly large bunches of 150 or more, since I have a big garden this isn't a problem. If you're going small go with a half pound of sets or plants you find locally.
With
peppers I have found the best producing are a variety called Ace. They are extremely reliable, produce early and are plentiful. Otherwise it is a crapshoot. I have good years and bad using most other kinds. Again you'll have to buy plants so local dealers will probably have what works best. If you're going to plant both hot and sweet, keep them separate or you may be in for a spicy surprise.
Potatoes should be started from certified seed potatoes bought from a gardening store, not the super market type. This will keep diseases out of the garden. As I said, I plant mine through plastic but if you want to hill them that's fine. Just don't plant them too deep and hill them too high. (Actually when I started my asparagus plot years ago I planted potatoes there first--the hilling and digging kept the weeks down.) Keep in mind too that potatoes take up a lot of room depending on how many you want. I generally plant less than 5 pounds of seed and they take up the second most room in my garden after the winter squash.
Squash is best planted in hills in sheets of black plastic and allowed to spread. I'm assuming you're talking winter varieties--butternut, acorn etc--that will need all summer to develop. Check the seed catalogs for "bush" types which don't need as much room or plant near the edge of the garden so they can run off onto the lawn. Most summer squash--yellow and zucchini--can be found in "bush" types that use less room. The same is true of cucumbers if you are considering them.
When buying your
tomato plants get them locally to avoid adding late blight to your garden. Again, given you locale, select early varieties. I am sure the local plant places will have a good selection for your area.
I've been veggie gardening since I was 6 and will turn 73 in 2 weeks. My current garden has be in the same spot for 49 years. It is great exercise and the produce makes for healthy eating. The hardest part is limiting yourself in both size and number of varieties. As you go on you'll add and eliminate varieties--I long ago gave up on sweet corn since it takes up so much room, the coons got it before I did and I can buy it locally cheaper than I can grow it. Order a few gardening catalogs and drool. Oh yeah, chickens and gardens don't mix that well so fence them out until the end of the season--once the garden is done then let the birds in to clean it of pests and leftovers.