I usually use contact cleaner (Honda's, which happens to be o-ring safe) and a small brush to clean the chain, and Honda chain lube after that. It's a messy job, so have a pile of rags handy.
Oh, and as to chain tension, riding with a tight chain is worse than riding with a loose one. You're binding your suspension travel and placing more stress on the countershaft than necessary...and it's probably why your chain squeaks. There's a damn good reason dirtbikers and roadracers have looser-than-normal chain tension. If nothing else, go to the loose side of factory-recommended spec.
-nominal_squid-
SMUSA #11