Aero is having a sale on uppers right now, and it seems like a good time to start this journey.  I'm looking for a gun to take to the range/ lease and just have fun with.  Also something that my kids might inherit one day and appreciate.
As far as I can tell, this parts list has everything covered except irons/ optics.  Am I missing anything or any recommendations?  Thanks!

Upper:
M4E1 16" 5.56 Mid-Length Complete Upper Receiver, w/ 15" keymod handguard 373.99 - http://www.avantlink.com/click.php?tt=cl&pw=55963&ctc=j0omgt4icr00zk8a02gtd&mi=13601&url=https%3A%2F%2Faeroprecisionusa.com%2Fm4e1-556-16-mid-complete-upper.html
Toolcraft BCG - JoeBob - 99.95 https://www.joeboboutfitters.com/Toolcraft_Black_Nitrite_Bolt_Carrier_Group_AR15_M_p/tool-tooauto-011bn.htm
BCM charging handle mod 4 - 47.95 - https://www.joeboboutfitters.com/BCM_Gunfighter_Charging_Handle_Mod_4_p/bcm-gfh-mod4-556.htm

Lower:
Magpul STR, dark earth - 71.95 - http://www.joeboboutfitters.com/MAGPUL_STR_Buttstock_Mil_Spec_Diameter_MAG470_p/mag-470.htm
Spikes stock kit w/ T2 Buffer - 67.95  https://www.joeboboutfitters.com/Spikes_Tactical_6pos_Milspec_Carbine_Stock_Kit_p/sp-sla500r-k.htm
Spikes Enhanced LPK FDE w/o trigger group 104.95 - https://www.joeboboutfitters.com/Spikes_Tactical_Enhanced_Lower_Parts_Kit_Dark_Eart_p/sp-slpk310.htm
Spikes Calico stripped lower - 89.95 - https://www.joeboboutfitters.com/Spike_s_Tactical_Lower_BLEM_Multi_Forged_CALICO_p/sp-stls016-blem.htm
Geissele G2S trigger - 156.95 - https://www.joeboboutfitters.com/Geissele_2_Stage_Trigger_p/ga-g2s.htm

Hey Patrick, you have pretty much everything set up right and it's roughly around $1,000 for this build but the problem I see is that although aero is a good company, you're picking up a $400 dollar upper (budget) and then spending $250 for a LPK and trigger, bad way to use the money because you can get something like an ALG ACT full trigger set boron coated for 100 dollars which is easily the best single stage trigger I've used and it's less than half the price of what you have there but with all the quality; a 2 stage trigger is pretty much for precision rifles and putting one on this build would just be a waste of money unless you're dead set on it.

Also I can't recommend BCM enough, I noticed you said you want your kids to inherit this one day and if you have the extra money I urge you to pick up an upper from them. You should probably get their LPK too it's just as good as the ALG ACT.

Basically my recommendation:

BCM 16 RECCE https://www.bravocompanyusa.com/BCM-BFH-16-Mid-Length-ENHANCED-Light-Weight-Upp-p/bcm-urg-mid-16-bfh-elw-kmr-a15.html
BCM BCG
BCM Mod 4 charging handle
(you can add the bcg and charging handle while you checkout the upper)

BCM ELPK (if out of stock get an ACT ALG lpk)
BCM buffer tube kit  http://www.bravocompanyusa.com/Stock-Hardware-Mounting-Kit-Mil-Spec-p/bcm-stock-hardware-kit.html
Spikes stripped lower
Magpul STR

While Aero definitely makes good parts, I would not place them in the same category as BCM. The BCM upper is reasonably priced, and combined with a Toolcraft BCG (good choice!) and a good single-stage trigger will give you a very nice rifle. Remember, the heart of the rifle is the barrel, bolt, and trigger. The lower is secondary; if everything is to spec there isn't much difference.

Good point regarding the trigger, thanks.  Being new, I still am not quite totally sure what I want where, and trying to hedge where I think it might matter.
BCM with the 15" KMR alpha was originally my top pick.  However, from reading to many forum threads, it seemed the consensus was either (a) BCM-awesome barrel or (b) BCM-great barrel but paying mostly for the name.  
If BCM is far superior, wouldn't my skill be the limiting factor for a long time and an Aero be a better fit?  I could spend the extra ~$300 difference in price on ammo/ sites.

Patrick, whoever told you you're paying for a name when it comes to BCM, they have no idea what they're talking about and have never touched a BCM in their life. You won't find rifles with BCM quality anywhere under $2000 and even at that price it's very limited and I would still always go with BCM. You make a good point about the $300 difference but like I pointed out you're overpaying about 150 dollars for your lower parts kit + trigger.
Just to break it down (even tho you probably already have):

BCM 16 recce upper + mod 4 charging handle + BCM BCG = ~$900 (keep in mind barrel is 17.5 inches with muzzle device attached)
BCM buffer tube kit (with H2 buffer) = $75
BCM enhanced lower parts kit -OR- ALG ACT elpk =$100
Spikes lower = ~$100
Magpul STR = ~$70

Total is close to $1,300 with shipping
Compared to your original being ~1,050-1,100 with shipping.

You are right about being able to spend the extra cash on ammo or a pair of irons but a set of magpul MBUS irons costs 70 bucks and ammo you can always buy a little bit every paycheck is the way I see it, I would rather have the top-tier rifle and buy ammo next month than to have a mid-range rifle and a bit more ammo.  I thought about going cheap too on my first build but after picking out this upper I can't stress how amazing it is. Also your skill wouldn't really matter in that sense.

you could save $20 (not factoring in shipping) and get a nitrated BCG with a C158 bolt at Monmouth Reloading.

http://www.monmouthreloading.com/shop/toolcraft-bcg/

I have no affiliation with Monmouth. I ordered one of these BCGs on Friday and the USPS tracking shows that it is supposed to be delivered today. Shipping was $6.41 with an upper receiver.