Another single homeowner here:
First, find the right handy person. Ask for recommendations in your neighborhood, where you work, etc. Walk around your neighborhood and ask construction workers/repair people who they use for different jobs. Actually go see work they've done if possible. Meet them and interview them. The price range for such work is huge and the variation in quality is huge, but in my experience the two are not necessarily linked.
My DIY ideas: For plumbing, I have found enough info on the internet to do something like repair a leaky faucet. You can google the brand of faucet you have and usually even see a video. Very helpful. (It took me 2 attempts, but I did it!) For hardware on a fence I would go to Lowe's, Home Depot, or my local hardware store. Hate to be biased, but I look for someone over 50 and ask him (so far it's always been a guy) how to do what I want to do and what the best hardware/fertilizer/lumber is. I even take notes. This has worked very well. I had the guy at the paint store tell me in detail how to paint my bedroom---came out great. (Before going, I researched paint on the internet--love Benjamin Moore Aura, low VOC) And I make a point of going back to thank these people when possible.
For the yard: I found that I am much happier with an electric (with cord) lawnmower for my large yard. It's light and easy to push and I don't have to fool with gasoline. For trimming branches, etc, I bought a small saw--one that really fits me. Get good tools, often available at estate sales.
Finally, someone suggested this on another forum, try to get a friend and make a deal to work together at one house and then the other---many tasks really are easier with two, and safer. (I only go up on a high ladder with someone else present, for example.)
I was given a DIY book, but it was so general as to be useless. Best of luck!