Jane, I didn't start as an adult beginner, but it's been at least 10 years since I was in the pool. I had to re-learn a few things. I agree that the spandex cap is better. It's easier to get on, it doesn't break, and it's more comfortable. The worst thing about swimming as a mature adult is the marks the goggles leave on your face. I don't remember them being this bad when I was in high school! I swim in the morning and usually they have faded by the time I get to work. Some people say the Swedish goggles with no padding don't leave marks. I also had to re-learn the flip turns. I watched this video and it really helped:
How to do flip turns
There is also a lot of good information for beginners on that Beginner Triathlete website.