1/8" chain with cogs and chainrings also 1/8" will give you the most secure drivetrain. But whatever you have, there are things you can do to minimizes chain deraillements.

Spin you cranks (with the rear wheel off the floor). You will see the chain go tightish then slacken. This is either the cog or the chainring not being a perfect circle centered on your BB axis. There isn't much you can do with the hubs/cog and they, even less expensive ones, are usually not too bad. Cranksets can vary a lot. Cranksets made for geared bikes may well be made cheaply with little thought or care given to making everything perfectly round and centered because on a derailleur bike, that matter not at all and may even improve shifting.

So ... you see the chain go tight and loose. Adjust your hub location until the chain has just a touch of clack at its tightest, then check to see how loose it goes. If the chain is within about 3/4" of play total up and down when tugged, you should be OK - if you do not have chainrings and chain designed to shift easily. If you do, change them! (And seriously consider spending the bucks to go 1/8") If the chain ever goes completely tight, it will shorten the life of the bottom bracket bearings and hub bearings a lot.

I've been riding fix gear forever. I love the ride. Never skidded. Always had two very good brakes. Always rode with good road tires and skidding would have put me in the poor house years ago. I have derailled a few times, sometimes (in fact usually) at high speed going downhill. It can get expensive. Paint, spokes, tire and chain usually suffer a little to a lot. (Better be carrying a bunch of dollar bills. You may well need them to stuff in your tire to get home.)

Ben