Well, I'm no expert, but here's what I do. Although I typically wash any dishes right away, if there is a time when I need to just put them in the sink and deal with them later, I make sure to run water into them so any food will be soft and easy to clean off later. I also wipe down the sink with the soapy sponge after I wash my dishes, to prevent having to scrub hardened gunk off of it later. For "real" cleaning of the sink, Melissa Maker at cleanmyspace.com (I like her articles... not really her videos) recommends equal parts water and isopropyl (rubbing) alcohol for cleaning a sink. It shines and disinfects at the same time.
(Not to get into a "you should eat like me" argument, but for numerous reasons beyond the cleanliness of my sink, I stopped eating all animal products and all oils a couple of years ago, and it has worked wonders for my dishes and sink, and my kitchen in general. It's so easy to clean when there's no grease! Everything is water-soluble and just wipes right off!)
Like you, I don't use our dishwasher, and I like the idea of getting all of the dishes done right away, rather than having them lurking in a dirty box under the counter. (My friend says, "Want a box of shit in your house? Get a cat!" I feel like dishwashers are sort of similar. To me it's a box of gross, dirty dishes, or it's a box of clean stuff hanging over my head that I need to put away. If I had a larger family, I might feel differently!) I was very against having a drying rack, too, but we recently moved to a new house that has no rack over the sink, so I've given in to having one on the counter next to the sink. (The sink is huge but doesn't have two sides, so putting the rack in the sink wasn't really an option unless we wanted to avoid using the sink for hours at a time while allowing the dishes to dry.) I don't actually mind it. I just give it a quick wipe/rinse every few days to keep the grime away. (Actually something I've finally learned to do with the rest of the house, too. A quick wipe here and there is so much easier than a weekend-long flurry of scrubbing when it becomes gross!)