The Giant is a great bike. And there are many many other great bikes available. The most important consideration is the fit of the bike, so yoyu should look at nd sit on and/or test ride a few before you make up your mind.
Cyclocross bikes like the TCX are a pretty hot item right now, but were less common 5 years ago. Therefore there may not be too many great deals on used models just yet. Other similar bikes are the Specialized Tricross, the Kona 'Jake' series, Surly Cross Check, and many others. Starting price for a new one is around $1000 or so.
While you are waiting for a used one in your siize to come available, you should figure out what is wrong with the Raleigh and sort that out. The skipping under hard pedalling might be a drivetrain wear issue; the 'jumping gears after backpedalling' might be caused by what is sometimes called 'a loose nut behind the wheel' (user error).