Neons are social (keep 10+ specimens) and very peaceful (don't keep with much larger fish or predatory ones, even Angelfish will eat them). Most people know they need soft water (certainly no harder than ~12 degrees dH, so they're poor companions for livebearers and other hard water fish) but less well known is that they need relatively cool water, 22-24 C/72-75 F. This is much like Corydoras and Danios, both of which can make excellent tankmates, but different to "hothouse flowers" such as gouramis and Cardinal tetras, so choose tankmates carefully.
Neons are plagued with one or more diseases called "Neon tetra disease" by hobbyists. The pathogen responsible may vary from case to case, but poor care, poor hygiene, overstocking and cannibalism are all important factors. Don't buy Neons from tanks with sickly specimens, and shop for quality rather than price. Once Neons start to get sick from "true" NTD there's almost never a cure, though antibiotics can help with the "false" or bacterial NTD. So prevention is better than cure. To be honest, if you have soft water, you will likely find Cardinals more sturdy, provided you can give them the warm conditions they need (in other words, won't be keeping them with low-end tropicals), and if you have hard water, then Neons aren't a sensible option anyway. I tend to recommend against Neons simply because the quality of the farmed stock is so poor.
Cheers, Neale