I HIGHLY recommend AGAINST the cheapest half sheet trays. I bought a pack of cheap chinesium half sheets that are basically garbage. They warp at 350F and are basically only useful as shelf liners and to hold whetstones.
That said, I have pretty high standards for half sheets as I use them at 500F to bake bread on baking steels. Its also very easy for me to tell if they warp because of that.
For half sheet, I just got some
vollrath 13 gauge that are better than the old ones I had. Don't get
Baker's mark half sheets. They warp terribly (twisting mode) when cooled too quickly. That is, if you pull them from a 500F oven and put them on a countertop, they will twist every time. Heating them back up untwists them but this is not ideal, especially if filled with oil. Normal half sheet cooling racks also don't fit in them perfectly; they're slightly too large or the slope of the sides isn't quite right. Nordic isn't bad. They're not as thick or have some anodized coating that flakes under heavy use. Nordic tends to bow in the middle like a drum. For bread, this prevents the bottom from browning. One of my thicker nordic pans twists when cooled.
I was looking for chicago metallic 1/2 sheet, but the thickest they had was 14 gauge and I wanted ones as thick as possible. Baker's mark was 12 gauge (but they warp) and vollrath was 13 (smaller number = thicker metal)
So far, I haven't had problems with my 13 gauge vollraths, but I've only used them a few times. Right now, those are the ones I recommend.
For quarter sheets, I'm less discerning. I have a nordic that was fine and I bought a few
baker's mark 16 gauge that aren't bad. I don't think quarter sheets matter as much for warping. I love quarter and eighth sheet trays for heating leftovers or pizza or roasting nuts. I have chicago metallic eighth sheet pans that are pretty nice but I don't think it really matters.
EDIT: Really it depends what you're doing with them. My use case (baking bread on very flat baking steels and shallow frying potatoes in the oven) is probably a tad extreme and my fanaticism reflects that.