With weight on your back, you'll have a natural tendency to lean forward to keep your center of gravity over your mid-foot. There is no need to exaggerate the forward lean. Just make sure to keep a rigid torso by getting your entire upper body tight. It may help to remember that the weight should be centered between the ball and heel of your feet.
Some people don't fully lockout their hips and I'm not sure how much it matters if they still use their glutes. IMO, it looks like your forward lean could be a problem in the future because it's not allowing you to get more glute strength into the movement. Getting your glutes involved will help with heavy weights and provide carryover to other lifts.
Any shoes that aren't squishy like running shoes will work. The best shoes for you are ones that allow you to lift the most weight without injury. I recommend trying shoes with and without heels to see what works best.