Dr. Ian Dunbar's After You Get Your Puppy is available as a free download - tons of great info on raising a puppy, stressing socialization and bite inhibition, along with teachng basic obedience skills (scroll down for pdf link): http://dogstardaily.com/free-downloads
There's more great free info at the top of the page under "Training Textbook". Dunbar uses "off" in place of "leave it", but even though I took Sirius Puppy classes which were founded by him and based on his books, I still use leave it. I use off as my all purpose command for getting off whatever they're on (get off the furniture, stop jumping on that person or humping your sister, lol!), rather than "down", as in get down off me, because down means to lay down.
One important thing to consider in advance is what commands you want to use to mean what things so everyone in the house is on the same page and consistent. You can have more than one command for a similar thing (formal vs casual command), but a command should never mean more than one thing.
Recall - Come, here, or something else. You may also want more than one command, a more formal one meaning run to you full speed and sit automatically in front, and one to mean get over here but not at any particular speed and not in any particular position. I use "c'mere" as my casual recall.
Heel usually means the dog is right next to you with its head at your pant seam, and a formal competition heel also requires attention. Many people have another command that's less formal and only requires that the dog be near your side (maybe within a foot or two) and not forging ahead or lagging behind. I use "lets go" for leash walks, only working on short periods of heeling at a time. If Halo gets too far off to the side, I use "over here" to bring her in closer, often with a pat on my leg. I also use "c'mon" a lot, especially on off leash walks at the park or around the house, meaning I just want them to walk in the same direction as I'm going.
Release word - I use okay, which is not generally recommended because it's used too often in casual conversation. I've never had a dog self-release, but I also say it in a different way when I'm talking to the dogs and I'm usually looking at them too, so they seem to understand when it's relevant to them and when it's not. Still, there are other good words to use, like free or release.
A great way to raise a well mannered companion dog is NILIF: http://k9deb.com/nilif.htm
It's easy to adapt to the age and abilities of any dog, even a very young puppy, and basically adds some rules and structure in a way that they totally "get", without punishment or force.