I have very heavy soil too, have found that the first year will be different as you adjust the soil. I would add sand along with the compost to help drainage (especially if you get some shade), and start off with unfussy crops. Avoid carrots this year, unless you want to double-dig. How about...things with roots "partly ready-made," like potatoes, garlic, onion sets (not onion seeds), or small-rooted things like beans and peas (their vines help do some of the stabilizing work of a root, plus their root nodules fix soil nitrogen). Be sure to remove all of the potatoes at the end of the season so that they don't pop up all the next year. You could even try a few strawberries if you feel ready for a perennial, they don't need deep roots either and have pretty foliage. If that is a sunny wall, you could also try a cherry tomato vine against a trellis on the wall, if you provide compost and keep it away from the peas and beans, as the extra nitrogen could make it too leafy. This is a more fussy crop but the hot stones would keep it warm at night, and it's very tasty so it might be worth it. Put in a fast cover crop like buckwheat when not actively gardening, and till it under prior to its forming seeds, to boost soil aeriation and nutrients. Have fun! :)

I'm afraid you have not given us enough of a view of the situation to warrant an "awesome" response.

From what you have provided, I would suggest building a raised bed, larger if you can manage to lose the space that apparently is more important as lawn. Once you have a raised bed, the soil you place in it will be the soil the roots will thrive in, above the clay.

(The problem with the clay is that it is composed of tiny particles of soil, without air spaces between, unlike the air spaces in your potting soil or in the compost and humus.)

You can put your little white plastic fence around the outside of it, if you like.

When you have children, involve them in all the outside activities.

Send us more information (photos) and we will give more awesome ideas.

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I know this thread is 1 year old, and you've probably moved off to college in a different country by now. But here's what I would do as a beginner vegetable gardener in a new country. I would NOT attempt 8 different things in the first year. I would attempt 1. And I would attempt something proven to grow in that cold climate, like Potatoes. No Rosemary, no Sage, no Brazilian Banana Peppers. Devote 1 year to getting a Potato patch going. If you can get that, then the sky's the limit in Year Two.

I live in the land of heavy clay soil, outside Atlanta, GA. Add compost, turn it up really well and grow some great tomatoes.

I come from the OTHER land of heavy clay soil, SW Ohio. Sheet mulching is what did it for me, and in a small space like that, its dead easy. One bale of straw should do you nicely.

just mix in compost and it works. or if you wish to skip all that trouble, just stack one or 2 bags of compost there. perforate the bottom for drainage, cut up a large hole on top and then plant. https://www.youtube.com/watch?v=81cWN8qYnds