Personally, I have a couple armorers wrenches and neither have I found to be particularly useful. (The fact that most of the handguard I use have a proprietary barrel nut probably has something to do with it).

What I have found useful:
1) a good vice
2) Geissele reaction rod
3) a quality torque wrench
4) a ar15 lower vice block
5) a good set of punches

 

A quality punch set. I’ve bent lesser ones numerous times. Depending on the brand of builders kit you will either be dealing with multiple roll pins or at least on the Aero M4/5 kits an Allen head slotted screw pin. Regardless my punch set gets used for all my firearms tinkering.

A buffer tube wrench. These are keyed for the castle nut that is used to secure the buffer tube. There are several brands of combo armorers wrench that have that feature.

If your assembling a free float hand guard then you need a either a wrench or socket tool depending on brand and model. When you mentioned kit, you did not say which brand.

A good quality torque wrench. All the info I’ve found suggests at least 30lbs. to tighten the barrel nut and using budget torque wrenches makes that a bit of a guessing game.

A good vise and an AR vise block for when you go to install the barrel. Make sure if your picking up a vise at the hardware store to order or get one that will open wide enough to fit the vise block in.

 

Most of your large online suppliers such as Brownells, Midway USA, etc. would have medium to high quality tools.

Some minor tools that I really appreciate are the front pivot pin installation tool, since I lost a few takedown detent pins before I got this tool.

Another one if you use standard mil-spec handguards are the handguard installation tool, some handguards are very tight and this tool really makes it possible to install and remove tight handguards.

Get an INCH pounds screwdriver torque wrench I have a digital Wheeler (there are other good brans out there), it is great for mounting optics and accessories.

Don't forget to use good barrel nut grease such as AeroShell 33MS/ 64 mil-spec which is what is recommended for AR-15 builds.

I also use medium type thread locker like Blue Loctite 243, good for optics & accessories.

For measuring parts I use a good major brand (Mitutoyo) caliper, micrometer and a scale ten thousand of an inch (Starrett).


Here are some sample AR torque specs, check the web (or YouTube) for confirmation of the data.

Torque Values:

Compensator (Flash hider): 15-20 FOOT pounds

Barrel Nut: 30 FOOT POUNDS Minimum, not to exceed 80 FOOT pounds to align the next slot in the barrel nut.

Carrier Key Screws: 35 - 40 INCH pounds.

Lower Receiver Extension (Buffer Tube):
Rifle: 35 - 39 FOOT pounds
Carbine: Tighten the castle nut to 40 INCH pounds +/- 2 inch pounds.

Head space information FOR 5.56 NATO:

New barrel Headspace: GO gauge 1.4636

NO GO gauge 1.4696

Field/ Unsafe barrel Headspace: 1.4730-1.4736"


(This information is provided for reference only and I assume no liability for the use of this information. Always double check the values.)

 

Lower Receiver Extension (Buffer Tube):

Carbine: Tighten the castle nut to 40 INCH pounds +/- 2 inch pounds.

I believe that number should be 40 FOOT pounds.

 

Magpul offers a really nice armorer's wrench. It's not cheap, but you shouldn't ever need to replace it.

Check out Midwest Industries' Upper Receiver Rod. It's an improvement on the Reaction Rod concept. Had I known about the MI rod when I was in the market, I wouldn't have bought the Geissele. The Geissele's a nice tool, but it doesn't stop torque from being placed onto the index pin.

 

The Magpul armorers wrench is the best I've used.

Geissele does make a reaction rod that takes stress off the index pin. Its what I use.

https://geissele.com/super-reaction-rod-5-56-223.html

 

All great recommendations above. I have built a few and have used a Wheeler AR Tool set. I added a 18" breaker bar out of my shop. I have 2 different AWs and only use them on the castle nuts. All of my handguards have their own wrench to fit their barrel nuts, hence the 1/2" breaker bar.
A good set of punches and Brownells has one for the bolt release pin that works very well.
A bench block for bolt and gas block work. it is invaluable to set the GB tube pin into position. I use a toothpick to align it all up and start my pin. the pin pushes the pick back out.
A stand with magwell insert, I have one with a bolt holder for disassembly etc
Gun Smith screwdriver set
inch/lb screw driver I have 2 wheelers and use them all the time
A little tackle box for all the spare pins and springs necessary. Brownells sells these in 3 or 5 packs sometimes. I have everything I need in small parts to keep my 6 ars running including spare bolts. A set of nut picks,

This is a start LOL

 

I have the Magpul and the Wheeler, they are different and the Wheeler came in my AR Armorers kit with a Tork wrench and the parts needed to put the pivot pin into your lower receiver and a work stand with a bolt clamp and other assorted tools. I set all my barrel nuts to 50 Ft/lb per recommendation from Aero Precision. I only use AP and BCM handguards on my builds. These 2 companies have top notch AR parts. The Aero lower parts kits include the screws and pins for the pivot and takedown pins. depending on how your lowers are configured.

 

My go to armory tools.

 

My go to armory tools.
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In your first pic, the box labeled "Flash Hider Wrench", the cutout you point to is actually designed to tighten the A2 rifle buffer tube to the lower receiver.

The box labeled, "No Idea Whatsoever", looks like it is to be used to tighten the locking ring on some free-float handguards that have cuts in the diameter for a spanner type tool.

The box labeled, "Must fit something", appears to be the size to actually tighten flash-hiders. If it is 3/4" wide, that's it.

I suppose I missed the spoof!! Have to quit taking some things too seriously.