@maxxblue : If at 60 you have not really worked out much, IMO, you are the perfect someone who would benefit from working with a personal trainer. I can't tell you how much my PT has helped me to achieve both my short- and long-term goals for my body. And my overall health. Which has proven to be just as important to me as what I now see when the mirror stares back.
If you hire a PT, find one qualified with some good references. The Internet is your friend here. Don't be afraid to do the research. It will be crucial to your fitness journey.
First meeting should be a sit down to talk about YOUR goals. Be specific. A good trainer will take the time to listen to you and then explain the journey required and map out the steps/timetable necessary to work toward achieving your goals. And he/she should also help you face reality; your goal may take a little longer now than it would have 20 or so years ago. Aging's a bitch, but I'm not going without a fight, lol! How about you?
He or she will teach you proper form when lifting; will put together a program for you to use IF you wish to work out on your own. Right now, IMO, lifting weights is very important; so is doing cardio and watching your diet. He or she can help you find the right balance to maximize your potential to reach your goal. It's amazing when body fat becomes supplanted by muscle. Woohoo!
A good trainer will give you honest feedback about your progress. What to change/tweak. It's why you'll spend good $$$ on a trainer; I look at mine like I look at my Doctor. They are both professionals, and I go to them because they are experts in their given fields. And they both have produced the desired results for my body.
But most crucial of all will be your stick-to-it-ness. You have to be consistent. Regular. IF you use a PT, you'll have regular appointments. If not, find a work out buddy. It's not so easy to blow off the gym if you have scheduled workouts. Find someone who will talk you off the "crap food" ledge if you need that. Someone who will encourage you when you may be weak. Or tired. Or whatever. It happens to all of us. And I speak from experience--can't tell you how many times I wanted to not go, only to feel so much better after I worked out. While there really is no magic pill to getting fit, showing up is indeed 1/2 the battle!
And that's exactly what it is--a journey. It will take time. Your body did not get to whatever shape/form it is now overnight. Nor will you achieve your desired goals overnight. You'll have peaks. Valleys. Highs. Lows. But that's what makes the journey so rewarding. It becomes part of your lifestyle.
I'm 64 now; like you, I had some man-boobs and other body fat issues; not anymore; my pecs, yes pecs, are solid and because of my genetics, round and, because of my PT, now full of muscle, not so much fat. I sincerely wish you well. Please check back with us and keep us apprised of your progress. Lots of great folks here. Let us help you as you begin your "manboobage" elimination and other body fat reductions! Good Luck!