Question: Should I spray some kind of weed killer or something on it before I get plants in there?
I would have sprayed the weed killer before breaking up the soil and then waited a couple of weeks to till it. Now I would just till it all in and do weeding when they pop up.
Looks like a nice sized garden plot. How big is it?
I would not because the chemicals will get into your food. If you are going to use a weed killer, the best time is the fall--after the harvest. That way, the weed killer will dissipate/dillute over the winter before the next planting.
Instead of spraying, remove the clumps of sod by hand. This will lower the ground level a few inches. But, turning over the remaining soil will fluff it up to make up for the lost height.
Do you have access to straw? You might want to start with straw bale gardening....if you research it you’ll see what I mean....plus it will hide those weeds/grass you are worried about and smother them for next year....just a thought.
Agree with the newspaper/mulch weed control. It’s cheaper (save your papers or have a relative/friend/neighbor do it) and bag your leaves and/or grass clippings or hay. We spread the newspaper and hay when we’re planting. Run a soaker hose down the row right next to the plants themselves. We leave about a 2-3” square around each plant unmulched.
If you’re anywhere that it might get dry this method saves big bucks on your watering bill, too. My parents had to water their entire garden 3-4 times a week down here last summer. We were once/week. In the fall, the broken down newspapers and grass/leaves/hay will be composted in your garden to improve the soil when you turn it all under.
We use cereal boxes and pasta boxes/etc around our blueberry plants and other outdoor things that get mulched with pinestraw as weed barrier. They *can* be used in the regular garden but break down more slowly. Depending on the length of your growing season they might not be broken down entirely by the fall.
YMMV.