Pop-wise, what is "high enough"? 3? 4? 5? More?
5 pop in the capital is a good size before stagnating to focus production on the NC, so work max food tiles within reason until you grow to about 5. This is starting area dependent, but is a good rough guide. With an all plains start with little or no good food tiles this might not be feasible and you may have to settle for slightly lower population which will cause a few turn delay in clearing to currency, not a game breaker or anything but you'd prefer to have a couple of good food tiles to get good growth.
How many workers do you consider enough? 2? 3?
Usually I'll get three, one bought, one stolen and one from liberty. If you decide not to steal, and save your free DoW for later preserving the diplo situation for longer, then it's probably a good idea to throw in a worker build at some point. Though 2 workers will not fail drastically at getting everything improved/sold. I prefer getting 3.
For this kind of start, would it be better to hard-build libraries, and go NC, or is the GL worth it?
The GL speeds things up by around 8 - 10 turns, and is available on all levels up to immortal. If you plan on playing deity then you're better off learning to play without it. With GL then you're definitely looking at slightly quicker than a turn 80 time on average to bulb chivalry, without it around the mid 80's is par.
Building GL for the free library and free tech seems like a no-brainer, but I wonder if this is where I'm going wrong. I don't want to have my stock strategy be dependent on something like a wonder that at higher levels, I may not be able to get. Would I be better spending those hammers on a worker, for more tile development earlier, then follow-up with National College?
If you're going to go liberty - settler, then you want to tech pottery - writing/AH (the order of these two depends on when you expect the settler to pop out, for instance if you find a culture ruin then you want to go pottery - AH) and plant the settler near horses. Buy the worker in the second city and improve the horses while building library. If you go liberty - worker, then you want to tech pottery - writing - resource tech, improve a resource to sell to help purchase library in the second city.
The slow down you're experiencing in clearing the techs to currency is possibly due to two things - low pop, as you said, but also a slower than optimal finish to the NC. So you may just need to tinker with things in order to get the NC built a bit faster. Library is your first priority in the second city always.
You didn't mention culture being a problem, so you're getting the cultural CS ally early enough to finish liberty by around 80 now it's just getting the order right in the other areas to time everything to finish together. good luck.