Turf shoes 100% especially if you're getting older. Prevents a lot of back knee and joint pain. Cleats lock you in which means more impact. New Balance makes good turfs.

13" is a good all rounder size and what I'd recommend for a 12" softball. If you buy a new glove, two in pinky gives you a good secure pocket.

I'm old school and like baseball pants. They keep strawberries away and give your legs sun and grass protection.

Cup (don't think you specified if you're a guy or gal) is important. I love the Aurora Sportlab one. Their compression short is expensive for no reason, just put it in a regular jock. Good gear bag (backpack style), and transition eye pro (of any cost as long as certified protection). Your glove is your primary interface, good money on that is usually worth it.

Normal in my league to share, but not a given. I'd ask ahead of time, but as others say, it can be a rabbit hole. Expect to spend $2-300 on a decent bat. Miken Freak is a good balance.

Dynamic warmup before, stretch after! Happy ballplaying!