wow, just wow.
you can get
a chain cleaner that works without removing the chain. they're decent and IMHO a minimum for a chain in the condition you describe. you will also need to use an old toothbrush and some degreaser (included in the linked cleaning kit) to clean the cassette, rear derailleur jockey wheel, and chainrings. spread out old magazines underneath the bike and you can do this even in an apartment.
there are many threads about chain lube. I hate lube that is too thin and too wet-- most of it flies off and what is left attracts a lot of gunk.
I use White Lightning Clean Ride, which is a wax-based lube and you have to apply and re-apply correctly. But when you use it properly, it stays grime free the longest and also doesn't need to be re-applied that often-- maybe once every 12-15 hours of riding.