Re: AR trigger
In terms of single-stage versus two-stage triggers...it really all comes down to a matter of personal preference as to which trigger you prefer as they are very different units. Here is a quick run-down I have posted in the past re: single versus two-stage triggers.
In terms of the operation of a 2-stage trigger...obviously, it has two portions that can be felt during trigger pull. The first stage has a much longer, generally heavier pull than the second stage. The first stage is normally called take-up (and some other synonyms) but should not be confused with creep or other slop in the trigger. At the end of the first stage, you'll experience a definite stop. This is the beginning of the second stage. At this point, you have "staged" the trigger and are ready to engage the second stage and fire. The trigger essentially works like a single stage trigger at this point. You should have a crisp, clean break with around 2.0lbs (give or take) of pressure.
An AR running a single-stage trigger will get you into a trigger like that found commonly on bolt action rifles. No creep, no slop, minimal reset, just apply pressure to the trigger and then break with around a 3-4lb pull or so (depending on the mfg). The 2-stage on the other hand offers safety and accuracy. You get a long, first stage with around 2.5lbs pull then a second stage with a crisp, clean pull similar to a single stage trigger, but with only a 2lb pull (give or take...the Geissele SSA for example is a 2.5lb/2.0lb two-stage trigger). You can't safely get an AR single-stage trigger much below the 3-3.5lb pull mark because of the risk of AD's, bump fires, etc., etc. The 2-stage triggers (some) are infinietly more adjustable to get a truly "tuned" trigger setup to the individual shooter's preferences. Take the Geissele for example...you can get a "Match" 2-stage trigger with a 2lb first stage with a 12oz second stage (infinitely lighter than anything you can get close to with a single-stage trigger).
The Geissele triggers are the cat's meow and are available in a number of different configurations, including adjustable/non-adjustable, varying weights of pull (total and in each stage), standard or flat trigger shoes, etc. I run a couple different Geissele triggers for various setups and they are by far the best bang on the market right now in my experience and opinion. While they exceed your budget somewhat, they are well worth the additional money. You can buy one from Midway USA and use one of the discount codes to get the price down somewhat (likely into the $180 range or so for the basic SSA), or you can get with various Hide vendors and see what kind of a price you can get on the particular trigger you want.
For a single stage unit, I run the Timney in a couple ARs and it is a good option also (and can be had for basically the same or slightly lower price if you can find them on sale).
Here are links to the two companies for you to browse at your leisure:
http://geissele.com/ https://www.timneytriggers.com/index.php?option=com_wrapper&view=wrapper&Itemid=17 Good luck!