What is the best way to prepare physically and/or mentally for basic and AIT?

FOR BCT---
Mentally:

You will screw up. There is no Ifs Ands or Buts about it. You will screw up. Try as you might, you will fail a task or two. BCT is designed to be a mental stress challenge. It's how you overcome those failures/challenges that will separate you from the adults and the kids.

Physically:

Between now and 15 September, I recommend you just to some workouts that will burn your muscles but not injure yourself. Don't overdo it. Don't over think it. No matter what you do, you will probably fail the initial APFT/ACFT (whatever they are giving new recruits). If you do fail, DO NOT be discouraged. Take that failure and learn from it. If you do pass it, then learn from that to do BETTER.

For your AIT---

Other than study your ass off, I have nothing to add.

For me basic training wasn't that physical. I went to basic at Fort Sill. Doing push-ups and running will help but I was in better cardio shape prior to bct. What I did get was stronger so make sure you're incorporating weight training. Especially since in basic your doing the ACFT which smokes your legs. Also work on your core. The hardest part about my basic was the cold. I've never been so cold in my life this far. The hurry and wait was pretty annoying too. And lastly, everybody experience is different. Every company is different. As much as you think you're prepared, you won't be. The physical is the easy part. The mental part is another story. Do what you're told. Try to keep a low profile. Show up 15 minutes early to every formation. If a DS say do 30 push-ups after every meal, don't cheat yourself. Do as your told and you'll be fine.

Whatever you do is not going to be enough. So just do more.

I thought I was so smart looking up manuals of my MOS only to get to AIT and find out that's not what they are teaching anymore. Whatever you think you are going to do to make your life easier some other idiot will ruin it for you.

When I was in basic I was 38, and had played the same mind games in a police academy. I knew what was coming down the pipe. We stepped off the bus to our training company and the sharks came out. They were yelling at us to grab duffel bags, and we were never fast enough, and had to start all over. I kept yelling at the kids to grab ANY BAG, and don't be concerned about YOUR BAG. Nope, no one listened. I was just another idiot, and it took me a week to figure out I should just let the kids experience this life defining event for themselves, and enjoy the show.

I made it a point to stay hydrated, always have a full camel-back.

You are going to do a million push-ups. The entire company could be prior service Ranger Tabs, and you are going to do a million push-ups. For them they would simply call it training/exercise. For you they are going to call it punishment. WHY you do a million push-ups is merely semantics. So don't get bent out of shape when you hear HALF RIGHT FACE!!!!!!!!!!!!!! because someone messed up. You were going to do them for something else anyway.