First advice - check lists of providers for your area and reviews for those providers.
We had American Home Shield. We had issues with our AC units a couple of times. They sent someone 2 hours away from us to do the service and they only serviced our city (70,000+ people) on Tuesdays. Fine except that in the middle of July and on a Wednesday, we'd have to wait or pay out of pocket. (Didn't matter if you complained it was an emergency at temps were in the 100's and kids lived at home.)
I understand that limitation and dealt with it.
My problem came with plumbing. We had a plumbing leak in the kitchen. Called in the request and no one called back. I had to contact them for everything. They finally, after three days had me contact someone. By this time, I had more than a faucet drip. I purchased a faucet on my own to install. When the plumber came, he followed their rules, but they would only allow him to install a replacement of their choice. (Mind you mine was purchased, wasn't going to cost them anything, etc). The plumber cleaned everything up and left it for my husband to be able to easily install the newer and better faucet. As it turned out, American Home Shield wouldn't pay the plumber as he happened to be on their list for our area and in order to paid, he had to be contacted directly through them.
Our AC went out again (same unit - 3rd time in less than 1 year), on a Wednesday and I called a local person. He reported lots of shotty work and showed us what really needed to be done - coils cleaned or replaced, leak in outside copper pipe. We decided on a new unit, but had AHS send out their guy, just to see what he would say. He filled the unit with freon, saying it was just a leak and "have a nice day". (So, not AHS's fault, but that was their only provider for our area.)
Home warranty was nice to have when we first got our home, but it was a bit of a hassle. I'm glad we didn't pay for it (well, not directly anyway).
We now have a warranty on our new AC unit and the same company has an annual service plan for our other unit. ($150/year if anything goes wrong and 2 checks a year). Wish we could find something locally for other things, like hot water heaters.
ETA: Don't go solely on reviews online. No one posts about the continued decent service they have been getting. It's going to mostly be negative and there's a LOT of negatives out there about home warranties.