I'm also 60, and a fairly new student. I grew up around planes, my father flew, and I with him as passenger and now and then got to "fly" but as expected it was like when your dad teaches you to drive...so not w lot learned except by watching, and spent my early years in a Cessna 172 with him.
But other than that no real extra "edge" except that I see small planes as inherently safe. Though I know well that the most dangerous factor can be the pilots skill.
Anyway, for me my first flight was like "coming home". Had been many decades since I flew with my dad and it felt so familiar. Of course learning to fly can overwhelm. Mostly I was also worried about my age. I learn things differently now than I did as a younger man. Also reaction is a little slower. Mostly I kick myself for not starting way earlier but I never had the extra cash, and when I actually could have swung it, it was not in my mind, I had kind of written off learning to fly as not doable. But then something jogged my memory and desire.
I can feel overwhelmed and see that in the beginning I was comfortable with flying, straight and level, shallow banks (10, 15, 30 deg.) etc. then slow flight...was getting used to it, but the CFI upped it, and was drilling me to different types of turns (level, climbing, descending) to different compass points, at different altitudes, changing it up. I think it rally only was a half hour and I was totally worn out, and felt like I didn't know what I was doing. He then said he thought I was doing really well. I felt I knew less than when I started. Got home, realized what I had to do. This I think is what folks here mean with getting ahead of the plane. When he tells me to "turn in 30 degree bank to the left, while descending to 2,500' while doing a 360" the first thing I have to find a ground reference that I will recognize when I have done a full 360, then look out for other traffic, then...
And as I get to leveling off at 2500 he may say "now ascend to 3200' while turning to 90 deg." Etc and I have to just think it through but with a plan.
Before I got the idea, I'd be turning 360 and he'd ask me if I had come around to the same heading...and I didn't know. Not using the compass, but ground reference. That's what he really wants me to get used to. But you still have to do checks, and also it's very hard but a necessity to look out for traffic.
Point is, where I would like to feel more comfortable with the maneuvers, he I think wants to both see how I react, and get me used to when things ARE overwhelming...where there is a lot to take in and do right. So he adds more and more any time I seem to be feeling comfortable. It's my theory anyway.
Anyway, I don't know how many years I realistically can have after getting my PPL, and am debating if even want to know. At 60, I think I won't have a chance to be as good a pilot as my father was, but the goal is to be a good safe pilot. Not do dumb things
Good luck to you! The main thing, all we can do is our best, learn at the rate we can, make sure we advance and learn...up to us really.