I've cleaned chains both off the bike and on the bike with the aid of the little three brush wheel gizmos. And being a year round commuter in a very sloppy weather part of the country I have to clean them a lot to avoid that horibble gritty sound. The way I found to be the least trouble and quickest was with the cleaning gizmo and using mineral spirits as the cleaner. The mineral spirits is re-useable for a LONG time if you pour it into an old pickle jar and let it settle out between uses. The dirt and grit settles to the bottom and leaves a clear tea coloured mix above which is fine to re-use a lot of times. And using the spirits means you can skip the part where you flush the water out of the chain that you used to rinse the chain with after the water based degreaser.

Using the gizmo and mineral spirits some loss due to dripping as well as blotting it off the chain using paper towels is inevitable but I get roughly a year out of a gallon of the stuff. And in my case it's used for a lot more than just cleaning bike chains. So it's actually a pretty frugal way to do it and not all that harmful to the environment when you figure you reuse it a lot. And when the solvent is just too muddy to settle any longer I mix it with the car and motorcycle drained oil for recycling. So all in all it is a cheap and effective way to clean that does not involve a big time commitment. I truly did find it faster to do it on the bike this way than to take off the chain and soak and shake it around in a jar. Much faster actually.

A good budget lube to oil the chain with after is the thick honey like chainsaw bar oil you can buy from Home Depot. It's less than $10 for a gallon of the stuff and that much will last you for years to come. Mix it 1:1 with mineral spirits and it thins it enough to soak into the chain easily and is still thin enough to wipe off the unneeded excess from the outside. I use this mix on both my 5 to 7 bicycles and my 4 motorcycles as well as mixed with a bit of STP as a bed lube for my metal lathe and mill/drill. I finally need to get another gallon after working on the first one for about 9 or 10 years worth of using the first one. The mix is also a handy round the house oil as well as once the MS dries away the light film of thick oil left behind doesn't run and drip. Great for squeaky door hinges, folding closet door quide wheels and anything else that moves and squeaks. It's not boutique'y like some options but it does the job and does it well.