You'll see your eels more if your lighting is dimmer. However, they are by nature ambush predators, so you are pretty much guaranteed that they will spend a significant amount of time hiding.
Don't get a Zebra or a Chainlink moray - they hide all the time, even after they get used to your tank. My personal experience is with a zebra and, more recently, a white-mouth. The whitemouth comes out a lot more than the zebra, but still only usually sticks his head out. I have heard that snowflakes are the same way. Basically, you're never guaranteed a frequently-visible eel. Your odds improve if you underfeed them.
Eels can get ich, but if they do it's likely a sign of bad water quality. If they do, treat with hyposalinity - copper is lethal to them. They are some of the most disease-resistant fish out there, and even quarantine fanatics like Bob Fenner (wetwebmedia.com) have advised that quarantining them isn't necessary.