The cheapest usable cellphone in Japan

Update

Now you can get a super cheap SIM-free cellphone in Japan by many companies (let me recommend "rakuten mobile"...), with a phone number and everything, so this is kind of outdated.

Japanese cellphone companies can be crazy.
They have some very hard to get bills, lots of plans which don't make much sense, and since the moment you sign the contract they usually will make you get in for some plans you don't plan to use but "need" to sign first in order for the campaign to apply, of which without it'd be even more expensive...

I used the Japanese company au's cellphone for a while, for about 7,500JPY per month. Then softbank, for about 9,000JPY per month...
That's pretty much my cellphone to receive emails, browse the web a bit while on the train, and get occasional phone calls. So it's pretty much a big waste of money...

Then, thanks to IP phones... we can get something a lot better, a lot cheaper! The services are:
Rakuten fusion smart phone (SIP phone number)
Rakuten LTE

LTE just refers to the (micro-)SIM chip you get to connect your cellphone to a Japanese cellphone network (docomo's) and use internet. And the SIP phone number is the thing that lets you do/receive phone calls via internet, you can also use it from your computer as you can guess (use Ekiga on GNU/Linux).

The SIP phone number DOESN'T have a basic fee per month. And you can make phone calls for free to most IP phone numbers (050- numbers). That means as long as you only receive phone calls, you'll be talking for free. And it's cheaper to make phone calls than from regular cellphone's phone numbers.
The bad thing, is that as you can guess, it relies on your network... If you are in a remote area, and your internet connection is kinda slow or doesn't respond very fast, you'll have a bit of a lag during the call. Kind of when you make a long distance phone call.

LTE works just fine, it has a basic fee from 875JPY to like 2,980JPY per month, depending on the bandwidth plan you choose. These are some very easy to understand plans...

The "bad" thing, is that you have to buy the cellphone in advance by yourself, and do the setup (put the SIM chip into the phone) by yourself. But that's pretty reasonable for the price you get, being that I pay like 900~1,500JPY monthly for this phone... about 6 to 9 times cheaper than I used to.

The cheapest ISP in Japan

The cheapest internet service provider in Japan has to be gmobb. It's great! NTT (the Japanese telephone company you have to pay to get the optical fiber router) doesn't have it in its double application list when you sign the contract, so you have to only ask them to have the router, or tell them you are going to use your own provider (more instructions in gmobb's page).
The only thing besides NTT you can use, is yahoo BB's stuff, but you obviously can't choose your own provider then... (and it's not cheap at all)
gmobb costs about 750y for optical fiber, this is as cheap as you can get.

gmobb also gives wi-fi access in BB wifi spots for about 300y. In which case you wouldn't need to call NTT (its router is over 3000y I think... don't remember, but it's what really costs money). But BB wifi spots are not that many even in Tokyo so you can't really use it as your main internet service.
BB wifi spots are usually McDonalds, train stations, and other restaurants/coffee shops.