i think mobility can be a bit harder to re-acquire with many years of disuse. carrying extra weight around can turn mobility drills into strength exercises especially when one is just starting out. bodyweight exercises tend to be hard for women in general and particularly hard when you are overweight. i do think that bodyweight exercises can be psychologically easier for women who aren't used to lifting heavy weights, though. you sort of don't realize how much weight you are lifting, if that makes sense.
squatting holding a doorknob for balance sounds like a really good idea, to me.
then goblet squats and / or squats where you hold the weight straight out in front of you.
goblet squats are really good for full range of motion mobilization (pushing the knees out etc)
holding it out seems to help with balance (making it a bit easier to keep the torso upright and engage abdominals than without any loading). nice way to transition into barbell squats.
when i started out (after many years of disuse) my freeweights program (though most of these were unloaded to start) looked something like this:
upper body horizontal / vertical push / pull
- overhead press (weighted of course. started with very light weights trying to train glute / ab activation)
- lat pull-down (eventually move to assisted chins then chins)
- push-up variation (start with the upper body up higher on a step or something then progressively lower it)
- inverted row (start with the upper body up higher then progressively lower it)
lower body knee / hip dominant (i think that was the idea anyway)
- static split squats (progress to lunges)
- air squats (progress to barbell)
- planks (for abs)
- stability ball back extensions (for spinal erectors / glute activation)
i did 2 days upper body (+abs) and 2 days lower body (+back) per week (alternating)
when i could get 10 reps almost comfortably would make it slightly harder.
i started out with 3x10 and it served me well.
once i was ready to get serious about the loading and strength (because the mobility was good) I moved to 5x5 (for strength).
i've read somewhere that 8-12 reps represents a good middle-ground between strength, hypertrophy, and muscular endurance. works each of them a bit so a nice 'generalist' rep range. higher reps (i think of 8-10 as higher) is good for greasing the groove / training activation, too.