>>2088454I don't currently have any raised beds in my greenhouse. Everything I grow in there is grown in tubs and buckets hydroponically. When I get a bigger greenhouse, I wouldn't mind some raised beds or homemade wicking tubs.
My first raised beds I made a year ago were out of wood, which works well and is easy to put together, but with the price of wood as high as it is, I've started using different materials. If you are able-bodied and have the means to transport them, concrete blocks are my current preferred method. It's hard work, but after you level the ground and make a few of them, you will feel like a garden-chad on steroids.
My beds range from one block high which is 8 inches, to two blocks high. My wood beds are made from 2x10 boards.
Placing them on the grass will be fine. You will get some long-rooted weeds, but it's not a big deal. Weeds will come no matter what. I tend to put cardboard on the bottom of the bed now, which helps a lot with the deep weeds.