I use progression and I've used strong lifts 5x5 in the past. I like progression with premium (it was like $10) because of the little graphs and custom workouts etc.
Tracking lifting progress is a weird one, because there are a lot of things one might want to measure, and some that would be interesting but especially hard to measure.
I've read that it is likely the rapid increase in weight one can lift early in a program is largely neurological adaptation. I'm not sure what one does with that.
Measuring strength increases is a little tricky. 1 rep max is one way, total volume is another, but it's easy to see how 10 reps at 200 makes more volume that 1 rep at 300, but more people can probably bench the former than the latter.
Muscle mass increase is hard. There are ways to fudge it, which I often do, but if you care enough, you may want to do dexa scans periodically. Most other biometric measurements are unreliable, although there is an ultrasound technique and dunk tanks that are reasonably good as well.
Percent body fat is another one people who lift like to track. That can also be facilitated via the scans above, but I often use appearance as a guide. Males with just visible abs are 10-12% bodyfat, females about 5% higher, varying degrees of vascularity and fiber visibility are cues about lower fat masses.
It could be fun to try to suss out the effectiveness of certain supplements. In the lifting community there are tons, but most have poor data and probably do nothing. Creatine is well documented and most swear by it, beta alanine probably is the second most attested....maybe others. Of course whey and pea protein (the latter for vegans or people on a budget) are almost essential if you're following most lifting protein intake guidelines.
Anyway, there's lots to track in this space, diet is at least as important as lifting in this space, and one really needs to know one's goals going in to know what to track. Good luck!