I use most any dedicated chain lube, preferring the tacky, messy kind. I'm currently liking the Maxima Clear Chain lube.
I lube immediately after a ride, but don't warm it if it needs it now.
The last chain was on a ZX9 (138 rwhp) that when 34K miles. I don't bother cleaning them very often.
I always replace the set, both sprockets & chain all at once. This is the best way to get the most mileage from a chain. I like the DID brand.
Maybe it's anal, but I also "break in" the chain by riding easy for a hundred miles or so; not wanting to "shock" any one section until it's had some run time.
Works for me.
2007 DL 650 with assorted upgrades