I mean, if I want to work towards proper lifting, should I start with body pump classes, or something else?
Thing is, Body Pump and proper lifting are two totally different things.
Body Pump is essentially cardio exercise, with small added weight, but you'd get pretty much the same effect using your body weight.
Actual weight lifting uses a different training method: you train to failure. You train each session to the point where you can't lift/pull/press the weight. But you do it carefully, slowly, and with correct technique. You don't bang out the reps. If you're lifting heavy, you maybe do 5 sets of 5 reps. You rest for up to 2 minutes between sets.
That is, you use what's called a 'progressive programme.' You don't lift more than 3 times a week (I do it twice, plus a Bootcamp class which uses relatively heavy kettlebells etc). And you plan each week to add a little bit more weight, until you reach the point of failure - without hurting yourself - so you take it sloooow. You might spend a lot of time on a plateau, building strength for the next step up.
For example, I hit a deadlifting personal best (PB) of 90kg a couple of weeks ago (I'm in my 60s - younger women can lift much heavier ,ore easily) and now I"m training multiple reps in a set (up to 5) at anything between 75 and 80kg. I do maybe 5 sets of 3-5 reps at 75 or 80kg, and by the 4th set I can feel the fatigue! So I know that keeps on building my basic strength for the next time I try to add a couple of kilos to the 90kg.
Squatting - I've been doing a lot of other stuff over lockdown, and since gyms reopened, haven't really focused on squats (b/c I love deadlifting!). Did weighted back squats the other day at 40kg really easily - 5 sets of 10 reps. Tired at the end, but felt good.
Before lockdown March 2020, my personal best 1 rep for a back squat was 62kg, so I'm training at 60% of my PB, and am actually coming back stronger - I did a LOT (I means probably hundreds each week) of bodyweight squats over the last 18 months. I'm now working on getting better depth (ass to grass) while not allowing my lower back to flex (I think it's called "butt wink") - when your tailbone sort of tucks under at the bottom of a squat. So squats help with mobility as well.
Also technique: the technique I see some individuals using in Pump classes is sometimes not good, and participants don't get individual, hands-on corrections of form, unless it's a mall class. Even then, I've seen people ignore the instructor's coaching & corrections, despite the instructor giving clear & expert guidance. Very stupid.