Any oil (not grease) used regularly will work fine... even wd40 (which really isn't a great lubricant, but better than nothing).
3 in 1 will work fine, as will tri-flow, even motor oil.
The most important thing is to keep it lubed. A bike chain is not a high tech device. It is not subject to extreme forces or temperatures. It's main enemy is road grit. Keeping fresh oil in there (the act of lubricating it drips out a lot of the contamination too), is the best thing you can do, trumping any supposed advantages of technique or product.
That said, buy a little bottle of bike chain specific oil or make yourself a batch in a oil dripper can (general formula is 3:1 motor oil: odorless mineral spirits).
Bike chain oil is more expensive than the cheapest alternatives, but it might be better suited than other oils in is ability to penetrate, not attract dirt and stay in place. My opinion is what you're mostly paying for is a slight advantage in functionality, but a good convenient dispenser. At the amoutn you'll use in a year, cost isn't a major factor.
Simplest way to maintain a chain: wipe it as clean as you can while turning the crank backwards (grab the lower run of chain with a handful of rag). Then drip oil into roller parts of links. The rollers are the only areas needing lubrication, so that's what you should aim for. Let it set for a while, then wipe as clean and dry as you can (agin, using a rag on the lower run of chain while spinning crank backwards). Get everything off the outside of the chain - oil on the outside doesn't lube, and only attracts dirt. Only the oil inside the roller portion lubes. You can't see it. A clean, dry looking chain can be well lubed.
I add one step to the above: After the first wipe down, I spray a thin oil (like wd40) liberally onto the chain rollers from above (remember, doing this on the lower run of chain), spin it a few times to work it into the rollers, let it drip as much contamination out of the rollers as possible, wipe it dry, then lube.
some people take their chains off regularly, soak clean (mineral spirits), hang to dry, and then lube. I do that once or twice a year depending on how much I ride (maybe every 7-800 miles).
I've used those chain cleaning attachments and think they're far more trouble than their worth. They are a real mess and my technique gets me plenty of miles out of my $25 chains. It's not worth the hassle and mess to try to make a chain last a little longer when they're not expensive to begin with.
Again, bottom line is lube it regularly. All the other stuff is minor in comparison.
