To attempt to directly answer your questions:
Liberty wrote: ↑Wed Sep 12, 2018 9:31 am...and take my time building it.
Good luck with that.
Lots of folks start with the intention of taking a year to piece together and AR and find themselves on the range within 2-3 mos.
My intention is to build a quality gun, but to keep the price down as best as I can.
This is certainly achievable, but price will depend on how willing you are to watch and wait for sales. There are a ton of people out there selling AR parts, and nearly all of them will be having sales between now and the end of the year.
The lower seems to me to be the best place to start...
Yes--the lower is a great place to start, and by the time you're done you'll have a better idea if you want to build your upper or just buy one.
I want a good quality casting, but is any one stripped lower better than another?
Not unless you like brand names and pretty engravings.
What should I look for?
As others have said, there's nothing wrong with an Anderson stripped lower.
I suspect that the plastic is not as ideal...
The modern polymer lowers are fine for most purposes, as the lower really doesn't take a lot of stress under normal circumstances. But since they're not any cheaper than a standard aluminum forging, they only make sense if you want to trade durability for mass.
Is there an advantage to the enclosed trigger guard vs. the milspec bottom piece?
The advantage to a built-in trigger guard is mainly that you don't have to buy/install your own. A flat guard comes in most lower parts kits, but installing it is the one place where people will occasionally break their lower. The ears that hold the trigger guard roll pin need to be supported well when you hammer it in, or you can snap it off. Very few people actually ever open the trigger guard to shoot--not a lot of shooting in mittens in Texas.
I am having a hard time telling the difference between a $39 and a $300 piece.
Unless they've done a lot of extra mill work to save a few ounces or it's designed for pistol calibers, the differences are all cosmetic. Some of the more extreme cases will actually make it difficult to fit some aftermarket parts (though that's more often an issue with uppers than lowers).