Its very easy to experience that adrenaline rush you speak of while travelling at safe, legal speeds as a beginner, and with bikes that have a lot of low end torque such as my SV650, its easy to keep it from fading.
The Ninja 250R is a great bike if you live in the US, but if you live in Europe or Asia it has a lot of viable competitors from companies such as Honda and Yamaha. Unfortunately only the Ninja is here in the US for some reason which really is just too bad.
I started riding about a year ago (almost exactly one year and one month actually) on my 2000 SV650. I bought it off a man who owned 3 bikes, 2 of which were set up for strictly track bikes. He sold the SV650 to me (the only unmodified bike he owned, save for a GSX-R600 rear shock) for $3k. It was fairly high mileage for a 7 year old bike, with 13k miles on it, but that was because he commuted to work on it and lived about 45 minutes from work, but it was well maintained. It came with a brand new set of Michelin Pilot Power tires on it (top of the line sport tires), and a brand new Yuasa battery. It was a sweet deal.