I use very cheap kitchen cutting mats often as my workstation mat. You can often get them for 2 in a package for a dollar or so. I get the non-colored translucent ones, so I can put a paper ruler under it, which I use to help keep lines straight and measure stuff right on the mat. I run a line of masking-type tape down the right and left edges, half on the mat and half on the table so the mat does not skid around under me when rolling and such. I cut right on them - although I try not to cut with the tip of something like an exacto knife on it, it will leave faint marks that your 'flat clay' pieces will pick up. Cutting straight down with a blade like it's a guillotine does not seem to mar it noticeably.
Sometimes I use a tile - you can get anything from 1 inch square to 12 inches square - one at a time at the big hardware stores like Lowes or Home Depot. Look for something shiny: tilt the tile so you see the light reflection off it, you want it as smooth as a piece of glass so it won't leave marks in your clay. I have found though that cutting on the glass tiles in motions like an Exacto knife can leave marks in the surface. You can also use ordinary typing-type paper or cardstock (with no lines, which might transfer to your clay) on top of your tile if you need to cut something. I prefer pure while tiles, so it doesn't influence my perception of the color of my clay as I work on it.
Tiles are handy to have if you are creating something that will become misshapen if you try to move it to cure it. Create right on the tile, just put the tile and all right in the oven, no problem. Be aware that the side of the piece touching the tile will have shiny spots - this happens when curing on anything shiny, curved or flat. Tiles, glass, light bulbs, metal frameworks, etc. If that part is going to be covered later, no problem. If it's in a place where you can sand it lightly later, no problem. You can TRY to USE it to your advantage to MAKE shiny areas on your clay, but it's nearly impossible to get the entire surface of the clay against the metal or glass - little pockets of air will be between the pieces and leave matte places. YMMV.
You can use a piece of glass, too: just be sure it's tempered and safe! We tend to put considerable pressure on our clay when working with it! Formica can be worked on, but I would not cut down into it, only run the blade flat against it to lift up a sheet of clay. Marble is nice, but be aware that marble is porous - if you leave clay sitting on it for any amount of time, the marble leaches the clay. And your marble will forevermore have an 'oily' spot on it. (.... ask me how I know...)
There are some wonderful more expensive glass type matts that are used in sewing and scrapbooking and card making with rulers marked under them, lines, and diagonal lines, etc. I have discovered that having a surface with perfectly measured lines on it already (or under it) can be amazingly helpful, but that's a whole 'nother story.
So it kind of depends on if you want to start out with high end stuff, or try some more inexpensive stuff until you get a sense of what works best for YOU. Even then, I suspect you'll move between a glass-surface type tile and a cutting mat type surface often.
--- Metal trays won't make it more likely to burn your clay while curing, that is dependent on the oven temps and if pieces are in direct line of sight to elements. Metal trays WILL leave shiny spots on your pieces, even round ones. And easy fix for that is to just line your metal tray with paper - typing paper, brown shopping bags (do they exist anymore?!?), cardstock. Paper does not burn at the temps you're using. The nice thing about metal trays is they usually have a lip on them, so it's harder for pieces to fall or roll off.
I apologize for my inability to be less wordy. Hope you got your questions answered. Hopefully more people will chime in!