Sadly a 30 X 30 patch of sun isn't going to do you a whole lot of good, since that patch will move with the sun angle, and your veggies need at least 6 hours of full sun per day up there in the northern tier. I think a long strip with southern exposure would gain you the most in the way of useable space. i.e. clear out trees to the south, east and west of the present open patch, and plant on the south side of that space as far away from the trees as you possibly can.
The edges of that patch will also be full of tree roots - don't forget most trees have roots out at least as far as the branches reach (cutting back the branches doesn't make the roots go away . . .
) As soon as you start amending soil, watering and fertilizing, those tree roots will just say "Yum, yum" and invade your beds.
Raised beds would make a lot of sense, too since even after you take out the trees you'll be fighting the roots for quite a while when you dig. The soil will be quite depleted from growing all those trees for years and years, too.
Another consideration is water supply - how close is the nearest water faucet to that area you want to grow?
Also, there are very likely deer and rabbits amongst other wildlife, so you'll need to consider fencing - really HIGH fencing! So the smaller, more efficient use you can make of your sunny space, the less work and cost it will hit you with.
How about starting out with some Earth Boxes? You can set them up on cinder blocks, so there's no issue with tree roots. You can also move them as the sunny area moves, and they're extremely productive in a small space. Also amazingly water-efficient. I know it's almost sacrilege to suggest not using "the land" but in areas with limited space, water and especially for you up in Minnesota, a very short season, it makes sense to at least get started with something that is going to work with what you have. You'd maybe need to take out fewer trees, too. All in all buying Earth Boxes might be more cost effective than removing trees, digging roots, amending soil and fencing in a huge area.
You could fence the sunny area you have, and plant your boxes for this summer, then spend all summer removing trees, digging roots and planning the bigger picture. You'll still get a harvest this year that way.
I can't guarantee you won't be simply hooked on the Earth Boxes by the time you have a bigger area cleared, though. It's a truly excellent growing system. www.earthbox.com
