I am still contemplating actually going back to D.O school - you are in good company.
So my opinion on training is something of a FUNCTIONAL one. I like to use and recommend exercises and activities that actually mimic(or partially mimic) human movement patterns. So the basics of these as you can imagine are squatting, exaggerated stepping(like lunging type movements) or and stair stepping stuff. THe other thing I like this for is that not only
are they human movement patterns that are familiar
both to you(so that you don't need to learn something complex) but also familiar in that its going to benefit you in your daily life.
All sports, ADLs and activities are based around these movement patterns both on the field(Obviously in combination) and in a training environment. So with this, the role of a performance professional, a rehab clinician or at the basic level the athlete, improving upon these patterns is what is going to get transferable
That said, I don't personally like to recommend the leg extension. I try to get people to imagine dragging a rope with a hanging sandbag(the lower leg) over the edge of a building. Plus depending on the degradation of the articulation between the patella and the femoral notch, it might not be comfortable. I personally don't like them for myself and I have healthy knees aside from 2 smaller meniscal tears in each and a little bit of recurrent patellofemoral syndrome sometimes with my left knee. They just aren't comfortable. HOWEVER, if you feel them working your quads, and you are pain free while doing them I would say do them if you like them. It does isolate the quad, but keep in mind, there is nothing else in the day, aside fromt that leg extension, that is isolating that quad. I would guess these might be a little uncomfortable for you, maybe not, but see if you like them and go from there.
So back to the stuff i would recommend doing - you need a cardio component. Remember that the aerobic system provides recovery to muscles while they aren't working(in between both sets and workouts) so increasing your CV performance is definitely
going to benefit you post surgically as well as during your workouts. For this I would warmup on the bike and get your body warm and the muscles warm. You could also do a portion of your cardio after
the weight training sessions.
Exercises I would suggest would be a lunge and some slow control stair walking, keeping in mind you need your knees stacked over your ankle as you step BUt more importantly making sure you just dont go in and start full lunging.
The lunge, just think of as an exaggerated step, which requires and BUILDS not only strength, but balance and general coordination. Start with something like quarter lunges, holding onto a railing, keeping your upper body tall. Then you can progress into lower and lower, making sure you are "stacking" the knee over the ankle.
The other functional basic I would suggest is a squat or a slight knee bend to begin then progressing. Here is a picture of a DEEP squat
but for you, actually beginning to assume
that position using that picture as the reference. Obviously don't go that far down, use maybe only a 1/4 or 1/2 movement - the picture is the reference of the chest up, knee stacked over ankle, hips back, back flat that is the "strong position" to teach to keep everything safe. Because you have a low back issue, you can modify this on a wall if needed. Put the feet about a half step in front, and slide up the wall as a modifier.
The finer pointers of these are making sure your hips are back and your chest is tall. The easiest way to teach this is to actually tell people to pretend there is a chair behind them and they need to sit in it, but not actually tell them where. The modification for these would be something like actually sitting in the chair, and doing "get-ups" ie. standing from the seated position to teach proper weight distribution on the heels, with the chest tall and the head up - NOT bending at the waist straightening the legs and reversing the waist bend.
Leg pressing is great as well, you can modify it if needed to do one leg. Just make sure that your knee tracks OVER your feet and that the knee stays stacked over the ankle - think of right angles.
I would definitely also work that ADDuction movement as well, focusing on smooth and controlled, QUALITY repetitions, making sure you realize you may be sore each time and that a big stretch may cause a little more soreness(its just tension under length)
Again Leslie for that leg extension I think doing isometric contractions(we call them "quad sets") of the knee when its in or near terminal extension. Working that terminal extension because when the quad KNOWS to fire in that position of extension before the replacement, actually getting it back and getting that terminal extension(Priority for TKR) you will already be a step ahead. So for these lying or seated on the floor, bed, table whatever you have. Leg straight out in front with a small towel underneath the back of the knee. Contract the quad, trying to press the back of the knee into the towel to get it into full terminal extension, hold for 10 seconds, then release the contraction. You can do these for sets of 10 sec hold, release for 2ish. The quads will get tired and "pumped" once you learn to activate them more.
A lot of information here: take it in and let me know what you think.