If you have 3K to spend, your options are pretty good. If this is your 1st bike ever, I would say stay 600cc and under. They are still plenty fast. You have probably already seen forums for new riders. We suggest you take a motorcycle safety course. Also, is your limit 3K including gear? If so, you need to set aside $400-$800. A decent (not great) helmet will cost you about $150. Try a HJC or Nolan. You can get some good big name (AGV, Arai, Shoei) helmets at the helmetshop.com for about $250. I also think as a minimum you need a jacket. Try ebay or newenough.com. A 2 piece suit would be better though. Plan on spending at least $250.
Now, if you still have 3K to spend, you pretty much have your pick of the 600's. I personally lean to the Honda 600 or the Suzuki 600, but they are all good to a newbie. A 1995 600 will go 150+mph, can do the 1/4 mile in less than 11 seconds (1-2 seconds faster than a Vette) and can go from 0-60 in less than 4 seconds. Plenty fast, HUH! Look for one that has not been down, has less than 20K miles and has been well kept. I also would not go for one that has a lot of mods. This may indicate it has been riden harder than usual. Get a friend who has ridden a while to test ride it. Make sure he takes it close to redline. It should be smooth and not vibrate alot. You should also ride it (easily) to make sure you are comfortable with it.
Then plop down your money and have fun!
Remember, life is a journey...do it on a bike!