This is PPOT, you HAVE TO get a Ducati 900SS.
I rode my Triumph today; every time I ride it I think about selling it for the first half hour or so. And the last half hour. Tonight I met some friends for a drink and, coincidentally, the Ducati Owners Club was having a night at the same bar. It was tough.
Like Sydney said, you can get into any kind of japanese bike for peanuts, and have a great time. I'm into my Honda about $1K, and it's a hoot, and has more than double the hp of my/your Triumph.
But, if you want some class for the kind of money you're talking about, you should at least go ride a 900SS; I've heard from a few fellas the air-cooled Ducatis don't break the bank quite so much as the water-pumpers.