I've had several nice bikes over the years. I bought a Legnano around 1976 from a friend who'd had it a few years. That was a nice racing bike - sew-up tires, etc. Very twitchy, though - I could never ride that bike no-hands. Super responsive, though!
I bought a Trek 520 in 1996. Not so responsive, but still not stable enough to let me ride it confidently no-hands.
Just last November, 2010, my Thorn Nomad MkII arrived. I've got a 38x16 setup on the gears, so I can climb the mountains. Very easy to get the front wheel off the ground! But also very stable steering. I can ride that bike no-hands easily, which I like. A nice way to relieve stress.
Whether your RST is the right bike for you, I have no idea. But many very fine bicycles have skittish steering - that makes them responsive, which has upsides and downsides. As for the wheel coming off the ground, that's mostly just low gears. Both attributes are things you can learn to work with. I agree with advice you've already been given - another couple hundred miles should help you see more accurately if the bike will work for you.