Welcome - started at 58yo.
Lots of good advice above. One more thought.
There is no "safe" bike path, because they are frequented by folks with dogs, pedestrians with small children and neophyte bike riders who don't know what they are doing and sometimes equestrians.
BUT, you can learn how to ride a bike path safely. Use a lot of common sense, be aware that children and dogs are totally unpredictable (along with some human adults), give lots of notice that you are there with a bell and yelling "passing" and further being aware that if they are wearing ear phones they probably didn't hear you. Don't be afraid to stop - and signal a stop so the quiet rider behind you doesn't hit you/ And, signal all your maneuvers such as turns. A bicycle is the ultimate stealth vehicle and EVERY time I don't signal, there is a bicycle behind me or overtaking me. I call it the theory of synchronicity.
Anytime you pass a young kid on a bike while yelling passing or ringing your bell, he/she is going to look back to his/her left and, at the same time, pull his/her bike to his left. Don't stopringing or yelling, just be aware of that instinctive reaction.
Horses tell where you are by listening. Ask permission to pass of the rider, and talk all the way through the passing. If passing while approaching, stop your bike and wait. Most horses are well-trained for paths, but not all. A friend of mine had his collarbone broken by a horse, and my wife was almost stepped on.
Anyway, there are a lot more tricks, but the above will get you started.
Have fun.
Last edited by DnvrFox; 05-28-12 at 08:01 PM.