Flat bottom trays work fine. You can buy what you need MUCH cheaper in a Walmart or somewhere that way, vs a photo store. To be on the safe side, get some gloves that are too large so you can get them on and off easily for rooting around in the chemicals. As Gerald mentioned, there are some that are not good to come into contact with over years of printing. Most people won't be affected by them short term, but the exposures are cumulative. In a world that exposes us to far too many toxic substances, why add these chemicals to your body? It's good safety practice anyway, as sometime you might be using something in or out of the darkroom that's much more toxic and you won't have to think about it, you'll automatically reach for some gloves.
I bought my trays in Walmart over in the household bins section, and ran a few beads of silicone caulk across the bottoms to keep things from sticking. The only advantage the proper photo trays have is a little lip that runs around the top that makes it a easier to hold the trays when tilting them back and forth when heavy w/ chemicals, and a small pour spout on one end for easier emptying.