I mostly agree with Albrecht's answer -- practicing is mostly for performance. If you're playing pieces for your own study and edification, practice individual pieces as much as you're interested in them. If you find a piece you particularly want to learn, spend more time on it. If you find yourself bored, move on (and possibly come back). The worst thing I think someone can do when beginning an instrument or returning to one is spend time doing things that aren't interesting -- it can easily ruin motivation and make it more likely you'll quit.
(I'm not at all down-playing technical achievement or competence. But assuming one has a good teacher or knows the basics already, those will come naturally by playing more. It's better to be motivated to play more rather than get bored or frustrated doing the same thing over and over unless you're interested in it.)
The question notes:
Right now I'm drilling away daily at one song (both hands, LH, RH),
but I don't have any fast reading or playing ability right now, so
I'm cautious of putting too many irons in the fire.
The only way to develop "fast reading" is through reading. If you're struggling enough to read the notes that you can't even play through the song or piece without stopping every few notes, then you probably need to keep reading a single piece or a few pieces for a while until you get those down. But once you are able to recognize most of the notes pretty quickly in a given piece, even if you're "stuttering" quite a bit while reading, you've probably hit the point of diminishing returns on reading ability for that piece for now.
So, if one of your goals is to improve reading, the way to do it is keep reading more music. (Again, I want to be clear this isn't at all to discourage more practicing to improve technical things, but if the goal is to learn to play and read more music, the way to do that is literally to play and read more music.)
How many should I add down the road as I improve? If I ever reach good
sight reading competency, does the limit basically vanish?
Yes, a good sight reader has very little limitation in terms of what to play, as a good reader can just pick up a lot of scores and play them right away at a reasonably proficient level. Of course, it's a bit of a chicken-and-egg problem, as to get good at sight-reading you also need to be able to technically execute music well too, which requires technical skills. And you only learn those through practice.
But my personal opinion and experience is that it's generally better to try to read more music and develop technical skills along the way, rather than focus on only one (or a few) pieces at time, if the overall goal is being able to play a lot of music. I've met many, many keyboardists in my life who are terrible at sight-reading music they've never seen before, and while they may be able to play piano sonata X by Beethoven and Y by Mozart at a really high level because they practiced it for a year with their teacher, there's always a huge barrier for new music, as every new piece is a bit of a struggle at first.
On the other hand, most of the excellent sight-readers I've met tend to be a little less technically focused (again, on average), but almost all of them enjoy exploring new music and just playing through new stuff on a regular basis.
Personally, I look at it as similar to learning to read books. Yes, you may spend a year or two as a child learning to sound out words, going through a sentence one word at a time and repeating the sentence (or paragraph). But after that relatively primary level of reading, the focus shifts toward reading longer and longer texts. You don't go back and "practice" reading the same book over and over after that initial stage. You stutter and stumble your way through more complex and longer books, and you gradually become a better reader, acquiring new vocabulary, absorbing new grammatical and rhetorical constructions and conventions along the way. You'll naturally become faster and more competent at reading, just by reading more. Meanwhile, most kids do acquire a few "favorite books" that they read over and over again at bedtime or something, that they'll naturally "practice" reading with -- which probably helps to cement some basic reading patterns with common words, etc. too.
Why should reading music be any different? Again, as Albrecht said, it's different if you're practicing for performance. (Just my own opinion, but I believe we put too much emphasis on this perfectionism with beginning musicians.) If we were training a child to learn to stand up and recite only one or two speeches -- rather than to read in general -- that would be a different thing. If you want to learn to read music (and enjoy exploring new pieces), I'd personally encourage you to keep reading and exploring as much as you'd like. When you reach a piece you really want to learn well, you'll naturally tend to practice it a bit. Make a list of those, and come back to some of each of those each day along with your reading practice. Along the way in those bits of practice you will gradually pick up some more technical skills.