I carry, a small adjustable wrench, a pair of pliers, a multi tool of hex and screw drivers, a bit of chain left over from when bought my new chain(I wouldn't expect you to have this but when you do replace your chain, keep those few links you take off,) a park tool chain breaker, a red and a black park tool spoke wrenchs(my front wheel needs the red which came with the bike, the rear that I built needs the black wrench.) These go in my pouch under my seat. I carry the adjustable in case I come across someone that has a flat but no quick release(happened yesterday actually. Schwinn cheap bike from a box store, tube was a 32c, tire was a 35c. I wondered why the tube was looking like it did until I saw the size and realized it was just coming apart. My patches wouldn't stretch to hold so she ended up having to walk the 5 miles.)

In my backpack pouch I carry a Quick Stick http://www.amazon.com/Quik-Stik-Tire.../dp/B000C128PC (I feel these are far better than tire levers and I have never gotten a puncture using these since there are no sharpish edges, and after you use it a few times, you'll see how fast and easy they make taking off the tire is, you only need 1) a spare tube, and a patch kit just in case I have more than one flat problem and the tube in case it is a valve problem. I also carry a smallish pump with attached gauge, I have a nice frame pump but it doesn't fit on my current bike so I had to get a different one. I don't really care much for short pumps but it works, surprisingly well too because it has a flip tab to stand on and it works like a floor pump. http://www.rei.com/product/648089/to...ump-with-gauge I don't want to have to make sure I purchase a cartridge to fill up for emergencies.

At home, I have a Craftsman allen wrench set with ball ends, a set of metric box ends, a few cone wrenches(more common sizes,) chain whip, cassette remover, bottom bracket remover(cassette and bottom bracket removers basically have male tabs to fit the female slots and a bolt for your wrench, whip is needed to grab a hold of the cassette when trying to remove,) and a crank arm remover. I also have a nice floor pump with a gauge. I do have a truing stand and dishing tool but that is if you want to spend that kind of money and/or lace your own wheels.

I've not had to use cone wrenches on my current bike, everything is adjusted with allen now that I have a threadless headset. Previous bike had the old style threaded steerer tube, and the smaller sized cones are really only good for rebuilding hubs but even then I'm not sure if they would be needed anymore(haven't rebuilt a new model hub so I don't know on this.)

For grease, I like white(milky white, haven't tried colorless but that is sometimes called white grease) greases with Teflon. I think greases tend to be personal preference. I've used a variety and just like the white because I feel it is easy to see. I have an older American Classic bottom bracket on my mountain bike that I would re-grease with a grease g u n(word filter is blocking it) and white grease made it real easy to see if I got all the dirty stuff out. Just been using white greases since. Wish I still had that grease g u n(word filter is blocking it,) can't find the darn thing.