I started weightlifting in 2005, and what's made the biggest difference for me in chest strength is bench pressing with the Smith machine. I use mid-to-heavy weights (enough to be exhausted around rep 15), and I do several sets - about 7-8.
When I started, I couldn't even lift the bar itself! Now I can plop the 35 pound plates on each side and go to town! I love the difference it's made in my life. Little things that I couldn't do before - like get my carryon luggage onto the top rack on a plane by myself or open jars (!) - are now possible. It's very empowering.
And for the record even though I've gotten much stronger, I still look like a girl, not like Popeye-in-a wig on or anything!
If you're going to bench press with the Smith you should probably get a trainer or a friend who's into weightlifting to show you how to use it properly. As with any weightlifting exercise, you need to be really careful and use correct breathing and alignment so you don't hurt yourself. I've hurt my shoulder before, and it sucked because it took months to heal.
Push ups are really great too. Start by doing what you can - say, 10 push ups. Take a short break, then do another set of ten. Do as many sets as you can, and as time passes you can increase your sets. Soon you'll be doing 50 push ups, girl!