I fly a Piper Lance, did most of my training and had almost 500hrs in a Piper Archer with no endorsements or retract time when I transitioned. It only took me 3 hours to transition. There isn't a massive learning curve going from a typical PA28 trainer to a PA32, a PA32 just flies like a heavy PA28. Your real stumbling block, as others have mentioned, is going to be insurance.
I might suggest a fixed gear PA-32.... the six/300 or six/260. Not as fast but without the retractable gear you're basically just flying a big Cherokee, I don't see why getting training in a plane like that would be an issue but I'm not an insurer. They may have other opinions.
If you are intent on going the retract route, see if your flight school has an Arrow or other retractable gear aircraft available that they'll give you some instruction time in. Having the retract hours will help you with the insurance company later.
In terms of plane shopping, first if you haven't learned about weight and balance yet learn it. Then go here
http://pilotfriend.com/aircraft performance/acft_list.htm and look up the specs of different aircraft types. And also go here
https://www.controller.com/ to get an idea what the market for that aircraft is like. I personally probably spent many many hours reading about different aircraft online and talking to other pilots/a&ps/etc before choosing what I wanted. Every airplane design is a tradeoff between factors like cost, speed, useful load, comfort, and other things. You will often find people in POA chat who will happily tell you how to spend your money and talk about airplanes.
Specific to my plane- the Piper Lance. The PA-32 series are known for high useful loads, mine is around 1400#. Once you fill the fuel tanks to the top that leaves about 850# for people and cargo. Again, this is one of the best piston singles you'll find for useful load. Yes, you can fly with less than full fuel but that creates other issues. Realistic true airspeed in cruise is going to be around 150kts, maybe better on a cold day or worse on a hot one. The turbo versions will go faster but will burn more fuel, have higher associated maintenance costs, and more complicated operation. Fixed gear PA-32s will be slower.
Also as I think others brought up GA travel is never reliable, you're ALWAYS going to be delaying for weather. Don't get me wrong, it's a much more fun way to travel and I do it this way for a reason but if you have to maintain a schedule and reliable travel... airlines, trains, and automobiles are better choices.