Greetings. I'm looking as well. I'm having a lot of trouble getting my initial choices to work on a new computer although an older version of one is working reasonably well on an older computer.
Although my situation is different from yours, I intend trying
Centos as soon as I've got broadband instead of dialup (since I'll have to download it and others for trial). It is designed for enterprise use (which means a reasonable period of updating and mending support) and it's derived from RHEL.
What you will find with most distros is that each version is like a meteorite. It flares brilliantly but briefly. Then the next version comes out and you have to start again because support (such as there might be) for the older version disappears. Unfortunately, the new version may simply introduce new problems.
Otherwise, for reliability,
Debian is out in front, from what I've read.
One good place to go for general information and links to more detailed sources is
DistroWatch.