Obviously, which you are doing, is to be looking at used bikes on Craigslist, garage sales, thrift type of stores, and maybe bike shops but these places tend to overprice them. I would recommend something more on the vintage side, meaning early 80's onward that is a steel frame bike near new condition rather than something more modern that is made of aluminium that the frame could be worn out...UNLESS the aluminium bike has been rarely ridden. I would recommend if you don't know what to look for in a bike and it's components is to either post bikes you find that you think will fit you here so we can advise you on it, or if you have a friend who is well versed on bikes including vintage bikes can locally advise you and even go with you to look at some.
You could try going to the group you're thinking of joining, or even that faster group as well, and asking them if they have an extra bike that is in your size that they're not using and wouldn't mind selling it to you. few of these people might have a stable of bikes and may want to downsize it and you could get lucky. The faster group may have a better opportunity for you because someone may have joined the faster group after buying a "faster" bike than they had before and now the old one is just sitting in their garage.
When looking for used bikes patience is the key, don't get into a rush. The good thing is due to your size small frame bikes do not sell for as much as the medium size frames due to demand.
New bikes in that price range are a lot more trouble than they're worth, so stay away from that temptation.
WARNING: I cannot recommend anyone buying a used carbon fiber bike unless you have a high degree of knowledge on how to check for possible damage. A lot of damage that occurs to CF bikes is hidden from view, sometimes the owner may not even know it's damaged that's how hidden it can be, most of the time they do know it's damaged but it's hidden so they'll sell to the unsuspecting fool.
