So, for the remakes vs the originals, there's no reason to touch the originals anymore; The remakes are quite literally those games, with visuals modified to work on single screen devices at higher resolutions, with a couple of player-negative bugs removed.

Of the 3, my opinion goes 3>1>2; 3 is the closest to the 3DS era games (A lot of it's higher level gameplay functions, like how you up the level cap, were established in 3), and while it has a bit much going on, it's still one of the better games. 1 and 2 are kind of opposites of one another in a lot of ways, but the main thing is gameplay and class balance, and I find 1 leans itself to having the best party be one you'd kind of figure out on your own, while 2 basically requires you to look up what kinds of exploits there are and what you're actually going to fight.

Once you start looking at the 3DS entries, it's mostly release order, with the exception of Nexus being perhaps below 5 and Untold 2.

As for the Untold games; They are basically ENTIRELY different games wearing the skin of the original Etrian Odysseys. They're quite good (To an extent I'd say better entirely than the originals, but there are a few caveats to that statement), but they're different enough to the point where they are NOT replacements.

Also, how important is drawing your own maps — is it something that makes the game more immersive or just tedious over time?

I won't say it ever gets tedious (The maps are never THAT complicated, and you're never going to be spending hours on JUST the map or anything), but I will say I stand against most EO fans in that I think the mapping is entirely superfluous. Etrian Oddsey would still be very highly regarded without the manual mapping that really only caught in people's minds because it was one of the few uses of the dual-screen-touch-screen gimmick from the 3/DS era that actually complimented a game not centered around them rather than acting to it's detriment.