You don't need a special bike for touring. You need a bike that you like to ride, and are happy riding for long enough miles on, and that can carry a reasonable load. For a lot of bike commuters, their regular old daily ride will do the job just fine. If you're car-free, your regular bike will do the job. The point where you might need to go bike shopping is if you mostly race or do club rides and can't fit a rack on there for love or money.

Most racks will easily fit on wheels ranging from 26" to 29"... wide tire 700c wheels are often called 29".

For panniers... are you happy with how the Ortleibs have worked? If they have been good buddies and faithful friends for dogs years, patch 'em up as best as you can, maybe wrap your stuff in stuff sacks or garbage bags, and give them one big trip. Duct tape, needles and thread are your friends here. If you hate them and would rather light them on fire than use them again, I'd look around for panniers that address the stuff you hate.

That $450 will vanish pretty quick if you don't have camping gear and want it... And it'd buy a lot of food, camping sites and motel rooms on the road. If money is tight, I would not be in any kind of hurry to spend on the bike if there's other stuff you would need for a tour.