Without repeating what others have said about the "assault weapon" terminology, your choice is going to have to be narrowed down to what potential needs you will have for such a firearm. Compromises must be made.
If you want a relatively inexpensive weapon that will take a licking and keep on ticking and also fires readily available ammunition that is not priced out of the ballpark go with the AK47. Neither the AK or SKS in 7.62x39 will ever be highly accurate hunting, sniping, or target arms but many feel it is the best compromise out there for your intended purpose. I've heard some fireams "experts" say if they had only one choice in a piece it would be an AK47.
My only personal combat experience is with the M16 and M14. The M16 was a great piece for delivering accurate close range fire and was highly effective within the ranges it was designed for. The ammunition is lightweight if you are going to be humping a lot of it, readily available, and again no more outrageously priced than most other ammo out there today. The Other thing to consider is that the ammunition would undoubtedly be more plentiful on the battlefield if the SHTF. The drawbacks are that they require constant maintenance and cleaning and from my personal experience lack the power and range to do the job in a lot of the terrain you will encounter in North America....that is if you plan to head for the hills rather than remain in an urban environment. IMO the caliber is ideal for closer range jungle fighting period.
If you are prepared to live with the maintenance and functionality problems associated with the AR platform you may consider either the 6.8mm or 6.5mm grendel. Based on US SOCOM field testing the grendel is about the most impressive all round caliber ever. It is both lighter weight so easy to carry but high velocity, accurate, flat trajectory, and has a punch comparable to the 7.62x51 at long ranges. The problem is it's a hotdog round, not available in great quantities, and priced through the roof. There are only two manufacturers chambering "AR style arms in this caliber and they are expensive. Have yet to have seen high capacity mags available for these. It's primary competitor to replace the 5.56mm in the US military is the 6.8mm. It is a slightly more effective round than the 5.56 with a slightly greater effective range, and is still far less heavy than the 7.62mm. My guess is, this is the one the military will go with...they always go cheap. Currently you can buy a Bushmaster with 30 rd magazine in 6.8mm for not much more than the Bushmaster and others of the AR type in 5.56mm. I'm still debating investing in one of these myself.
My favorite combat caliber by far is the 7.62x51mm. The natural choice in that caliber is the M1A1 but it is a battle rifle, not an assault weapon. Much of what has been written about the reliability of the AK47 can be said of the M14. They have been well tested for function in adverse conditions. Of what's available they are about the best compromise for range, accuracy and stopping power. But they are pricey and if you are going to be humping enough ammo for an all day fight you're gonna feel it. Personally I would rather compromise a little and instead of planning on the 25 to 30 fully loaded magazines with an AR, I'd go with a plan to carry 6 to 10 with an M1A1.
Another piece to consider in 7.62x51mm is the FAL. It is reliable, accurate, and combat tested. Lots of mercenaries prefer them. The FN FAL is getting harder to find but here is a picture of something that is available...I am seriously considering this one. A very reasonable price if you ask me.
View attachment 20658
Item# FAL Imbel .308 Battle Rifle $919.00
Brand: Miscellaneous .308 Rifles
FN/FAL Imbel .308 Battle Rifle, semi auto, these rifles start as original imported Imbel part kits , they are factory built on a Metric Entreprise Arms type 3 receiver made of 4140 steel by Entreprise Arms , the rifle is totally refinished in Mil Spec Zinc Phosphate ,they feature a 21 inch threaded barrel with a Zero climb muzzle brake ,original synthetic stock set, weight 9.8 lbs ,length 43 inches , ships with owners info , 20 round mag and backed up by a limited lifetime factory warranty. These are a resonably priced FAL factory built rifle and not the junky worn out part kits guns built by others.
Please understand I am no expert by any means. I am still learning here. The info I provided is basically what I have gathered by reading a lot...my personal research to decide what I will purchase.
My personal choice will be either the one pictured here or the Bushmaster 6.8mm.