If you are interested in a Speedmaster Chronograph you have to be very careful, as there was a series produced that has major problems with chrono hands not engaging and other issues. They can be avoided by checking the serial number, but it is definately something to be aware of if you're buying used.
The non-chrono wathces don't have any issues like this, and generally make great watches.
The great thing about buying a used Omega is that the price probably isn't going to fall much lower unless you break it. This means you can wear it for a while amd then easily sell it for as much as you paid (or more) and try another one out.
I would highly advise you do two things:
-Educate yourself about these watches. Learn the models, history, and technical features and get a good idea of what a "fair price" is. This is the best (really the only) way to protect yourself from fakes, as the accuracy of Omega fakes has gotten extremely good in recent years.
-Don't buy on impulse, take your time and find one that you really like. Impulse buys are a sure way to get burned when it comes to watches.
Out of curiosity, just what is it about the Speedmaster in particular that made you choose it over other watches?