I used to grow a lot of wheat grass. If you soak the seeds overnight and then spout them a day or two you will cut down on the grow time severely.
Flats work ideal. Use new soil each time. You don't have to fill them all the way, an inch is plenty, then cover with just enough so you can't see the seeds and place a layer of plastic over the tray. As the seeds grow they will push up the plastic don't remove it until they are a couple inches tall. Usually on their next watering.
I would never give them a second cutting. If you go to a feed store you can get a 50 lb sack for almost nothing. Winter wheat works best but you may want some variety. If you give them a second cutting you will be paying more because you will wear out your juicer. You don't need to give them much light and you can start them on a lower shelf and move them to the top as they mature. If I remember correctly they only took 4 or 5 days to mature and got too tuff to juice much after that.
What I did was to plant in half trays and start a new half tray each day. So the first day you got a jar of seed soaking, the second day you got one jar soaking while the other is sprouting... the third day you've got one try planted (half tray in my case). You should wind up with about 4 trays growing, 1 sprouting and 1 soaking. On days you don't juice you usually have to throw that days tray away. Usually I wind up throwing as many out as I juice. Sphagnum peat is cheap, easy to find and works very well but they sell two kinds and you need the one that is ground up or you'll be spending all day breaking it up. The one I buy says premium on the label and one bail is enough to last several seasons.