That's a solid routine sounds a lot like Starting Strength. I'm unfortunately not built to squat, my hips don't like it and I have disproportionately long femurs. I am going to add in some Zercher squats as deadlift assistance.
Hacksquats are great for the quads.
I want to progress to the clean & jerk, as a one size fits all compound exercise, but my gym isn't really set up for it (its a commercial gym) :(
Does your gym have kettle bells?
Occasionally I'll do a modified power snatch. I'm doing the deadlifts almost like a short high pull, and will do a set or two with a snatch width grip.
Clean and jerk has a lot of technical components but generate that initial velocity is key.
That is what I focus on in my dead lifts, maximizing explosive force for the bar to the top of the quads as quickly as possible, while making sure it "rams" solidly into my quads, via hip thrust
I have a 16KG kettlebell at home & 4kg kettebells too. My gym has tons of kettles.
Once a week or so I'll do Kettlebell swings with the 16s or 20s, that seems to be good for snap and velocity, and cardio :)
I'm older (52) so I do my strength training after cardio.
Kettlebell swings are great. I aspire to still be lifting when I am your age. I'm the underside of 40 (only just) - and want to build as much of a strength base as I can before I know it will decay. I walk 25 min to the gym, so that's my warmup & cool down. Only drive if raining.
That's a solid pattern.
Exactly that :) I've started again last Dec after about 3 years off lifting. I am ALL leg in terms of my height (just over 6ft / 180cm) and I find sumo squats to be the best compromise for me - the traditional leg machines just don't "work" for me with how long my legs are!