Just try some squats with no bar now. Keep the chest up. In fact, lift your arms forwards, keep them parallel to the ground and your head up looking straight ahead.
As you descend into the squat, at some point you'll feel yourself get a bit less stable. Your knees might wobble, you'll feel the urge to bend over to balance. Don't. Just keep chest up and knees out.
That instability is the "core weakness" Morgan spoke of. Like other kinds of weakness from being sedentary this disappears pretty quickly. In a month or two you'll be going straight up and down without trouble, nice and deep.
The width of stance isn't an issue, you'd have this difficulty with your heels together or wide apart like a sumo. But for bigger and taller guys, a wider stance is often more comfortable, with a narrower stance your gut gets in the way. Sorry I don't know how to put that politely.
Film your deadlifts, too. If you're rounding your back on squats you will almost certainly be doing that on deadlifts. You may find sumo deadlifts more comfortable. With big blokes, as they descend to pick up the bar, the belly gets in the way, makes them put their knees out, so their grip has to be ridiculously wide. Having the grip inside the knees sorts this out.
As with squats, so with deadlifts - "chest up!" Again, keeping your back in extension is most important. You may not be able to go all the way to the ground with your back in extension. That's okay. If you can't, begin with the bar around your knees. The progression for you then, instead of increasing weights and reps, will be increasing reps, and increasing range of motion.
For everyone, more weight, more reps and more sets are progressions. For the beginner, more range of motion is, too. It's not as satisfying as whacking another 10kg on the bar, I know. But it's a progression, increase safe range of motion and you're getting stronger.
I wish you were in Melbourne, mate, I know just the bloke to introduce you to, client of mine. He's an IT and rpg geek, too. And he's got stronger and dropped some weight off.