You're a beginner, beginners don't usually start training for racing until they've ridden for at least a year and put some miles under their belt. If you are an athlete now, like running a lot every day, then you could get into training for racing sooner, if your not an athlete now I would be concerned about you getting burned out fast if you jump with both feet into training and racing before you put a year on a bike.
Used racing bikes, like ones made of aluminium and carbon as Campybob pointed out are too tricky for a beginner to inspect for frame problems. I suggest getting a steel bike they're easier to inspect for damage, like rippled paint is big clue, or the fork doesn't line up perfectly with the head tube, it appears like it's pushed back toward the down tube; the rear tire is too close to one side of the rear of the rear stays, though that could be due to the wheel not being in the dropouts correctly. You can train on a steel bike, you can even race on one, you can get a set of racing wheels for race day which would help a lot, then as you get better in a couple of years you can find either a used or new aluminum racing bike and still use the wheels you bought for your steel bike to race on the aluminum bike with.
I recommend that a amateur racer use nothing but an aluminum bike, why you scream when CF is lighter? Because as an amateur racing alongside other amateurs who don't know how to hold their line, don't know how to stay off the rear tire of the rider in front, don't know how to communicate they're going to move out from behind another rider and pass, don't know how to control the bike on fast turns, etc, etc, etc, all that means there will be a lot of crashes, and crashes result in a lot of broken bikes, thus by having an aluminum frame bike you could get another frame for less than half the cost of a CF frame. Even pro races there are a lot of crashes, magnify that by about 10 times and that's what an amateur race will have! Difference between a pro crashing and destroying his bike vs an amateur crashing and destroying his bike is that the pro gets an entirely new bike for free whereas the amateur has to pay for his new frame (frame only because you can't afford an entirely new bike) out of his own pocket. On top of all that, you'll need, or should have, a backup bike for racing, in case you do wreck while training the day before the race you now have another bike ready to go on race day, or if you don't you're out of the race. Plus you need a set of backup racing wheels, and wheels get damaged a lot, so you have to another set always on hand ready to go just in case.
There is a lot more to racing than meets the eye that I haven't even mentioned, amateur racing today will cost an average of $6,000 to $8,000 a year, that doesn't include the bike(s)! That's tires, repair stuff, gas to travel to events, motels, coaches (trainers), event entrance fees, food, and other costs. You could do it for less if you all you want to do is race in your local city's events, but as time goes by that won't be good enough...I know, I've been there!
Later when you get really good at racing one of two things are going to happen if you go beyond Cat 3. You will need a better lighter more aero bike so CF will be the frame to get, and or if you and your team are really good you can sometimes get a partial sponsor, usually bikes only, and sometimes entrance fees, you still have to pay for all the other stuff I mentioned. Till you go pro then all that stuff is covered.
