So Earthbound Beginnings is Mother 1, where Earthbound is Mother 2.  Not a prequel, but originally produced first.  So I'm guessing this means that it is best to play Earthbound Beginnings before Earthbound.  Am I correct in saying this?

The games are barely related story wise, so it doesn't really matter.

Pretty much, the original Mother has aged very poorly, next to unplayable if you aren't used to playing 8bit RPGs.

I would say skip Earthbound Beginnings, it's too similar to Earthbound but worse in every way. I thought about getting Earthbound Beginnings so I watched it a little and read about it and it's not worth it imo unless you're really hardcore I guess lol. I love Earthbound btw, one of my favorite games.

Mother 1 hasn't aged well compared to EarthBound, and I heard that Mother 1 is actually pretty hard.

I recommend trying out EarthBound first, then Mother 1.

I think you should do EB first. If you start with 1 first, I think you're going to have a bad time... It's fun to play it and see what it's like, but it's hard. Like, NES hard.... x (

Earthbound is much easier to get into. Mother 1 is a bit rough around the edges and has some pretty nasty difficulty spikes.

If you are going top lay Mother 1 anyway, play it first. You won't want to go back after playing Mother 2. Same can be said about Mother 3.

If you're gonna play the first Mother, make sure to increase battle text speed to cut down the grind.

Nah, I'd say play Mother 3 first. Eartbound is a better game.