However I'm pretty clueless on recovery - other than a cool down at the end of the session. Unfortunately I tend to go straight to work and sit at a desk all day and I'm finding that my muscles are very sore by the next day
That's just DOMS (a fancy name for soreness of muscle when you use them in unaccustomed ways) - the best remewdy is 'active recovery' - the nest day. A long walk, a swim, more exercise of a different kind.
You also need to look at your cool down: is it a good 15-20 minute stretch of all the major muscle groups you've pushed in your session?
I do 2 PT sessions a week, which combine heavy lifting (I'm failing at deadlifting 100kg, but training to lift that eventually by lifting reps at 90k) with metcon - yesterday it was 25 cals on assault bike followed by a minute of dumbbell thrusters, followed by a short run, followed by 25 cal on the SkiErg, followed by a minute of burpees, and rise and repeat for 25 minutes.
I then stretch for 15 or 290 minutes, also using a foam roller. I work through:
kneeling quad & hip flexor stretches, into the splits, then into the pigeon pose, then stretching my knee to chest & across my body, then rolling out quads, calves, hamstrings and IT band. With a lot of child's pose & down dogs in between each held stretch. I usually finish with a few back rolls over into the plough pose as this really stretches out my back.
I'm an ex-dancer though so i'm stretching to maintain flexibility as well. But all of those stretches - except for the splits and possibly the Plough - are good for anyone. Hold them for about 5 long breaths, using your breath to relax through into the stretch.