This simple and effective programme will work for just about everyone - including you oldies. I got my parents to start pedalling, and they now go over the mountain passes here in the Alps, and recently they even managed the 100 mile trip around Lake Geneva. It may be obvious, but if you want to race you must actually go out and do it. We women know all about being nervous to the point of not even starting. Get over this silliness and participate.
Cyclists are generally very friendly people.
This is where to start. For racing on the road you need a typical high quality bike. Ask at your local club, as all cyclists love talking about bikes. You may even find that someone has an old bike they re not using which can be checked over and leant to you to get you started. Some things are essential though.