"- you do not need a lockring. Lockrings are only useful for young and suicidal dolts (with attitude) who ride fixies without brakes. They stop by hopping the back wheel. This tears hell out of the rear tire, and it requires the use of a lock ring. In my 35+ years of track ridng and racing, I have never used a lockring, and I have never had a cog come unthreaded on the track, because my first track coach (a former pro 6-day rider) taught us to never, ever backpedal a track bike. However, be sure to tighten the cog with a chain whip or cog tool. You do not have enough leg strength to tighten a cog while riding."
With no disrespect... some of this is bad advice.
And I am neither young, suicidal, or a dolt... but I log a lot of miles on my fixed gear bikes and build a lot of them for other folks.
When you ride a fixed gear in an urban environment you may put some resistance on the pedals to control your speed, (even when you have a brake) and without a lock ring you could spin the cog off the hub... and this would be a bad thing.
You can get fixed gear parts in 3/32 or 1/8 specifications and either is fine if the set up is correct... my new work bike is spec'd with 3/32 parts as is my fixed folder.