Upon moving to Japan, a phone number is one of the first things you need to obtain, as you will need it to obtain a bank account or rent an apartment. The 3 major carriers are SoftBank, Docomo and AU. Check this article for a general introduction to the Japanese mobile system. The downsides of signing a contract with the big 3 are that they are expensive, have long contract times (usually 2 years) with high cancellation fees, and may only offer foreigner-unfriendly methods of payment, such as via a Japanese credit card or transfers from a Japanese bank accounts.
As a result, most foreigners use MVNOs when they first enter Japan, as they are better in all the aspects mentioned above. Check this article for an overview of the more popular MVNOs. I will discuss the 2 MVNOs that I've used personally, GTN Mobile and IIJmio.
GTN Mobile is one of the few MVNOs that offer English-language support. In addition, they allow payment using foreign credit cards or at a convenience store. These were the main reasons that I chose to go with GTN Mobile when I first entered Japan. To sign up, I went to their office in Shin-Okubo.
GTN Mobile is on the SoftBank network. People here seem to diss SoftBank somewhat, but I personally never had problems with connectivity, even on trains. Of course, I'm located in central Tokyo, so maybe the connection would be worse if I had to travel to the suburbs.
A more unique benefit of GTN Mobile is that they have a tie-up with EPOS card to offer their customers credit cards. Getting a credit card in Japan is notoriously difficult, and I was actually rejected by EPOS when I applied independently. However, having a Japanese credit card is very helpful as some businesses will not accept foreign cards. So it may be a strong reason for a new arrival in Japan to go with GTN Mobile. Mercari helped us apply for the SMBC Prestia card, so it was unncessary for me.
Support-wise, GTN Mobile was responsive and helpful via email. I got replies within a day or 2 at most (and in English!). However, one thing that was not great security-wise was how they handle payment method changes. When I wanted to change to credit card payment, they gave me the option of sending my credit card number via email or reciting it over the phone. The former is terrible, and the latter still isn't great if you have to make the call in a public area (which will probably be necessary since they only operate during working hours).
Another downside is that they do not seem to offer Mobile Number Portability (MNP). This means that if you change to another carrier, you have to change your number everywhere, with your bank, credit card, landlord, workplace etc. I luckily had no issues doing so, but it's possible that some Japanese systems are so outdated that they won't let you change your number. That, or if you forget to change your number before switching carriers and you have 2FA via SMS for some services, it would be a problem.
The main downside of GTN Mobile is that compared to other MVNOs, they are more expensive. If you look at their plans, there's a whole bunch of numbers which may seem confusing. But the gist of it is that "Premium Start Support" means that your data will be tripled for the first 2 years, then return to the base number (the smallest one). Once all the discounts expire, you pay 3580Y/1 GB, 4580Y/3GB, or 6580Y/ 7GB. In contrast, most MVNOs will offer 3GB at under 2000Y. The exceptions are Sakura Mobile and Mobal, both of which also offer English support. So basically, the MVNOs who target foreigners charge you a premium.
The good thing is, GTN Mobile has a short contract length (7 months). So once the contract period was up, I switched to IIJmio, who just happened to be having a Golden Week campaign at the time where they waived their signup fees.
First of all, IIJmio does not offer English support, though they do have a website in English. The account page is Japanese-only. You can sign up online or at a store (e.g. Yodobashi or Bic Camera). You may be able to find English-speaking staff at more popular outlets. However, I went to the Yodobashi in Shinjuku and the staff member there only spoke Japanese, so your luck may vary. The staff wanted both my residence card and passport, but they let me sign up with only my residence card.
IIJmio's prices are pretty reasonable. I pay 1728 a month for 3GB of data on the Docomo network. You can also choose the AU network (type A), but I went with Docomo (type D) because they have wider coverage. However, because they are an MVNO, they have limited bandwith from the parent carrier and I sometimes notice slowdowns in speeds during peak hours. However, basic usage like texting on messaging apps will still be ok.
IIJmio's contract length is 12 months and they offer MNP, so I see nothing to complain about there.
The main problem I have had with IIJmio is with payment and credit cards. For starters, they only seem to allow payment via credit card. However, they do allow foreign credit cards, which is helpful. My foreign credit card was accepted, but my Japanese SMBC Prestia credit card was rejected for some reason. As I did not want to pay for expenses using a foreign card, I applied for another credit card (UC Gold) and was able to use it for payment.
If you do not speak any Japanese, GTN Mobile will probably be an easier experience to sign up with. However, you will be paying more for less data and the lack of MNP makes switching troublesome. If you want an MVNO with English support and MNP, Sakura Mobile is probably a good choice.
As for IIJmio, my only real concern with them is the drop in speeds during peak hour. But for everything else, it's a viable carrier for a long-term stay in Japan.