I use the 3/4" thick mats from TSC. They are very durable and don't slip a lot, YAY! I've used others that were horrible for slipping. I'd vote for shavings if you can buy them in bulk or pellets if you can't. Reason I say shavings in bulk is because I can buy a year's worth of shavings in bulk for what 1 pallet of the bagged shavings will cost me. If you can't buy the shavings in bulk or if you have no place to store them, then I prefer pellets. Put down several more bags than they recommend and pick every day. They last a LOT longer than shavings before you need to strip and rebed, so they're more cost effective.
STRAW SUCKS, IMO! I use it when I'm foaling but as soon as the baby is a month or so old, I go back to just shavings. Straw isn't very absorbent and it can weigh a TON when it's wet as well as being stinky. I just put down my last bale of straw for the new foal today, and when that's done he'll be a month old and I'll be back to just shavings. YAY!