My personal experience as an exchange student might echo or differ from some of the posts already made in this thread (after a day of serious storms here, I'm kinda tl;dr right now) but I still want to share:
We as students looked over all the carriers in general and decided that AU made the most sense for us price-wise and service-wise. This is because DoCoMo is way overpriced (we're talking $100-200+ a month), mostly because their selling point is that they still work even when the subway is moving in Tokyo (which is silly to buy it for when you can just wait 45 seconds until you stop at another station and you have a signal again.). Softbank seemed better for those who wanted a prepay phone (which one or two did get, but I think their services were limited), but their coverage wasn't that great. AU, while they didn't have a signal while the subway moved, seemed to have equally good coverage as DoCoMo with better prices better than both them and Softbank, and had a wide range of services. AU was a two year contract, but we realized that if we tried to do anything less than a proper contract with them that it would cost us more in the long run than the $150 to break the contract at the end of the year, so we opted for that. AU phones run off of an ICID card (if I'm remembering correctly) that acts as a key to allow the phone to work in the AU network. Without the card (which looks like a sim card), the phone is pretty useless beyond its preinstalled apps. When you break your contract, they remove the ID and all your emails and addresses are still intact, but after a couple of months my phone started to go a little wonky without it.
Speaking of the phone, when you sign the contract, you have a selection of free phones like with US/Western carriers. AU only had one bilingual phone to offer, and it was one that was designed with middle aged people in mind, but it worked just fine for me, and even with my fellow students who got phones that weren't bilingual and that did more things (like radio and tv), I was able to get more use out of my phone in the long run and my phone looked a little more high quality, haha.
I got my phone apart from the majority of the other students and went to the AU store with a friend who was a former JET oddly enough. My friend negotiated my phone for me, and the salesman was so impressed that he gave me a discount, haha. This being said, I do suggest bringing a friend who is either a native or fluent speaker of Japanese with you to the store so as to circumvent awkwardness/frustration in filling out contracts and answering questions.
Another point is how Japanese cell phones are actually used. You do not make phone calls on your phone. Talking on your phone in public is considered really rude. Because of this, phone contracts come with virtually no minutes. If you try to use a japanese cell phone for calls like a western one, you'll be paying hundreds of dollars a month unnecessarily. For sanity's sake, I opted for having the 47 minute plan. I think everyone else took the cheaper 17 minute one. Your phone is used to send emails and surf the net mostly. Net use is charged by the packet sent and/or received on a yen or fraction of a yen basis. For example, say you send an email that ends up sending 27 packets to the server and say your rate is ¥0.2 a packet. 27x.2=¥5.4 is then what you're charged. I can't recall how packets are calculated, but it's like a few kilobytes or something. If you just stick to emails and occasionally checking the weather channel, with a 47 minute plan your bill will come out to around $45 a month for your phone. As I did see someone mention early on about jerky cell phone salespeople, if someone isn't going to give you a proper contract, I would personally leave the store. To prevent someone being a jerk, this is also why I suggest bringing a native or fluent Japanese speaker you can trust with you- they'll help you to not get ripped off and get you off to a good start. I've personally never run into jerky salespeople at AU, and bringing a friend who is fluent helps reduce the stress of "OMGGAIJIN" when you walk in.
When you receive your bill in the mail, all you have to do is go to your nearest convenience store (as long as it's listed as ok on the back of the bill- generally 711 is the place to go), and as you're shopping, put your bill on top of your items of purchase and the bill will be added as part of the price. You pay them (cash), they stamp your bill in two places, hand you back the stub, and you've paid your cell phone bill. Incidentally enough, you can also pay your utility bills in the exact same way. It's pretty nifty. Don't be afraid when you have to thumb out ¥30,000 on the counter for bills, though. It's normal, and you're not going to get mugged on your way out.
I would not buy a phone from another jet, simply because you're going to want a new phone with your own email address that won't get confused with your pred (basecode for the root email address for the phone doesn't change no matter what you change the actual user address to, if that makes sense. In that way, you give your close friends your basecode address and everyone else your flavor of the month user address- if you think you might not want to talk to people later, haha). Previously I wouldn't have recommended getting an iphone for japan simply because I couldn't see how the functions of the iphone would be useful in the ways that are specific to Japanese phones, but in the past couple years this seems to have changed and the iphone has become pretty much the same it seems. So, unless your pred is trying to sell you an iphone, I would probably just start from scratch when you go to the carrier's store, haha.
After you cancel your contract, you keep your phone. I still have mine, as senile as it's become since leaving japan. I still charge it up every now and then to look at all the pictures stuck on it, because the phone companies have conspired with the major micro SD chip makers so their phones will only take the $40 name brand chips (like sony or sanyo) instead of the larger capacity, $5 ones from china, so all my stuff's still stranded on it, haha. Your Japanese cell phones will NOT work in your home country most likely. I know the US, for example, uses a different wavelength for cell phones than japan does, so they're incompatible.
This post has become pretty long. Sorry about that. But this is everything I can suggest and share at the moment about cellphones in japan. Hope it helps give some idea of what it's like!