For cleaning the grill's exterior: soap, water, a rag, and elbow grease. If it's old, a very little bit of WD-40 where needed, wiping it down with a rag when done. I avoid any degreaser/WD-40/Soap residue near any of the food cooking surfaces or interior. As others have said, once you properly break in a grill, it shouldn't ever look brand new again.
For the interior: once a year I take everything out and vacum the inside good with a shop vac, empty and clean all the grease catches if any. Then I super-heat it, usually a little less than an hour before I intend to cook. From there it's pretty much what I normaly do when I BBQ, take a wire brush and give the pre-heated grill you'll be cooking on a good scrub without cooking yourself, I also try to knock down any balls of grease that might be forming on the underside with the brush, then wait another 5-10 minutes before starting to cook (burn off the stuff you just knocked down).
I don't like instant-light charcoal myself when able to use a chimney device (not gonna lie, love them) or even old-fashioned lighter fluid (you control how much fluid is used). The chimney devices look flimbsy, but they're really good once you have some practice. Basicly they're designed to drop down the ignited coals when you lift the device up from it's resting position. The trickiest part is not using too much newspaper and not using too little. It doesn't take a lot, but it needs enough to just start, and it's very easy to use too much newspaper and choke out the oxygen flow when you try to ignite it.... and then it gets flimbsy and clumbsy-like as you try to stuff or remove more paper into the bottom of a device designed to drop-down the coals that it's holding up with one smooth action (picking it up). If done properly, the bottom most coals in the chimney light and it quickly (2-3x quicker than if they were in a "pile") works its way up and ignites the whole cache, then the top ones are white on the corners, lift the chimney, it dumps the coals safely, you do a little spreading, and you're good to go. If you need more charcoal than your chimney will start, simply pile it onto the lit stuff and resume your standard OP.
