I've only completed two previous builds, one being a pistol and one rifle in 5.56. Both were pretty much budget guns and that was all I was really going for. I want to build a rifle now for long range shooting and was thinking of going with a Grendel. I don't want to throw only cheap parts in this one, so my question is what should I be looking at in a lower? Is there a huge difference in paying $39 for an Anderson vs $100+ for some other brand? Would it be fine to go with the Anderson and then spend some money on better parts to go with it?

Also, I'm thinking of a 22" upper for this build, any suggestions on brands or where to look for them?

The lower is not critical as long as it is in spec. Just put a decent trigger in it. Geissele is having a 15% off sale on their Web store.

As for the upper, just get this 20" complete upper from Alexander Arms. AA is having a 10% off sale, but I think it ends in the next couple of days.

You'll love shooting Grendel.

Looks like they have a good amount of triggers to choose from. Any recommendations on which one for this kind of build?

The G2S for $140 should be fine. I have a couple of the SSA-Es which are very similar. All the Geisseles are worlds better than a standard AR trigger. The ultimate is the DMR, but you don't need to spend that kind of money for a great trigger unless you absolutely have to have one that breaks like the proverbial glass rod.

You can go to any of the main dealers right now for a decent barrel.  There are two camps, the SAAMI only camp, and the as long as it's accurate camp.  I'm a "as long as its accurate camp". There will people that come on this thread and say "SAAMI only or there's no way it can shoot".  Prepare yourself for the commercial and same 10 pictures.

I have a non-saami chamber and I just have to use the right bullets and the proper seating depths.  I can shoot 1" 10 shot groups at 100 yds with my ammo that isn't sorted for component weight, and is loaded using a powder thrower.  I love the 3 shot group advertisements, rarely do you see people offering up 5 shot groups to display their rifle capability, and even rarer is a 10 shot group.  Anyhow I'm sure if you buy from a reputable barrel maker you will be a happy dude.  For non-saami you have BHW, Saturn/Liberty, and Maxim Firearms.  There are a few more you'll find too.  Then for SAAMI you have Precision Firearms, Alexander Arms, I'm sure there are a couple more but there are less SAAMI barrels available than non-SAAMI it seems.

I am personally waiting for a barrel maker that is releasing a new bolt and extension this summer.  He will be also selling .264lbc barrels with this heavier duty bolt and matching barrel extension.  The cool thing about this setup is that it will be stronger than standard bolts and if you want a spare you can still use a standard 7.62x39 bolt.  I plan on buying a spare specialty bolt from the get go, and if I need to I might buy a LMT Enhanced 762x39 bolt as a final back up.

As for a trigger I havce a Hiperfire EDT in one lower and have a Geissele Super Tricon in my other lower.  Both are nice, the super tricon is a bit nicer than the Hiperfire.  The price difference though makes the EDT trigger attractive at $100.