I'll Third Shawn's and Spped's excellent suggestions, and Second Jamie's fantastic Triumph idea... with a slight
caveat.
I too have seen far too many guys buy big, expensive, heavy bike's (or tempermental "exotics") as their first ride, then quit in disgust because they can't "make it happen" like they saw on TV somewhere! In the USA, there are thousands of super low mileage big bikes available... for this - and other - reasons.
Buy something lighter, comfortable and easy to manuever for your first ride. The "Cruiser" style bikes (Triumph America, Speedmaster) are the easiest to ride, as the center of gravity and seat height are super low to the ground. This is why you see so many women and beginners these days riding "Cruiser" bikes - low seat, low CoG. In a few years, you can trade up if you wish, or sideways, or whichever direction you may choose.
The Bonneville is an excellent choice as well, but for a "beginner" bike, IMHO the middleweight / lightweight "Cruiser" style is easiest to learn on. America's and Speedmasters are plentiful on the second hand market, and reasonably priced right now. Lots of Honda's and Yamaha's in the "Cruiser" type mode as well. After say a year of riding this first bike, you'll feel more comfortable, and at ease with riding, and by then you'll have a clearer idea of which direction you want to go... bike-wise!
I would also highly recommend a riding course from one of the local Safety Foundations. Look around.
If buying a Triumph :
1.) As Jamie noted, '09's and '10's have EFI (Electronic Fuel Injection). A very nice welcome to the 21st Century, and trouble free.
2.) Ask around, research around, and find a good dealer. Most, but not ALL are... good. A bad dealer can ruin the experience quickly. Get more than one recommendation, maybe from three people minimum. Visit a dealer and hang around for say an hour or so. You should get a pretty good picture from the overall atmosphere of the shop, how visiting Customers are treated / reacted with, and the attitude of the employee's.
3.) Don't buy a bike that has been highly modified. Try to find a stock one, maybe with aftermarket silencers (Arrow?) at the most. Stock = reliable.
4.) Low mileage is best. Remember that most Triumph's go in for an expensive service at 12,000 Miles (Valve Clearance, etc.) unless you are mechanically inclined, and can do such things yourself.
In the end, you might want to define what
YOU are looking for in Motorcycling. Long trips? Daily commutes? Day tripper? Weekend racer?
If you look around, you'll see an infinite variety of Bikes... and riders, all seeking something we presume. What are YOU seeking? This decision may help to further define your first purchase bike style.
Most of all, Ride Safe!
Bob
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and would like to become a moto-rider.
what motor to take, my 2 fav are 
