I'll try not to repeat what others have said. In addition to simply riding as much and as often as you can until your trip, I would try to find a bike maintenance class. Many bike shops offer them. I would also find, if you can, a bike safety class. Short of that, you would be wise to find some experienced riders to show you the ropes of riding in traffic and on busy roads. You need to know the rules of the road, along with the protocol of riding with other cyclists, down solid before you leave.

For gear, I would get the best shorts you can afford, a couple pairs of gloves, sunglasses, a good fitting helmet, bike jerseys, waterproof jacket, gear that can help you through chilly mornings like arm warmers and knee warmers, cycling shoes (along with clipless pedals), a bike bag (or two), and water bottles and/or a camelback, and plenty of socks. You'll also likely need some chamois cream, sunscreen and ideally a summer weight long sleeve jersey. The chances of you getting a saddle sore are high, so you'll likely need something for that. I use benzoal peroxide (zit cream) for mine with good success. I'm sure I'm forgetting other pieces of gear that would be helpful.

From a training perspective, try to do back-to-back long rides to get your body used to, not only riding, but riding when tired. You're also going to have to learn on the fly how to hydrate and eat when riding that much. It is SO easy to get dehydrated on a multi-day tour. You absolutely have to drink on and off the bike ALL the time. Once you get dehydrated, it's really hard to get out of that hole. Eat regularly on the bike and you should be okay.

I see that you're riding east to west. Yike! Is there a reason for that? Wind is not going to be your friend. Most xcountry bike tours go west to east for a reason.

Good luck. I hope you enjoy it and are safe.