I get veges from the grocery store, co-op, or farmers market when that's open. It kind of varies depending on where I'm doing my regular grocery shopping and I just browse the available veges and pick out what looks freshest each week. I try to change it up as much as I can but stick with what looks fresh. I'm able to keep greens fresh for a very long time by cutting the stems out and putting the greens in a quart ziploc with a folded piece of paper towel and storing that in the bottom bin of the fridge. I put a date on the bag and can often keep greens fresh for a month.
As far as food in the beard goes you can sometimes see it when they open their mouth. If you move their beard around a bit with your finger it can bring it up and they'll start chewing it. If the beard just feels like loose skin though, that's a good thing and probably is just that.