Japan has a few MNOs and a few MVNOs. As a foreigner (assumably, an English speaking one primarily), I do have some advice for what you should and shouldn't get.
For MNOs, order of preferences based on speed, coverage, in Tokyo etc:
au (KDDI)
You can use povo2.0 if you want the au network without the payment issues from au. povo2.0 is “prepaid” and an “MVNO” but they sell data toppings that are valid for as long as 1 year, so you could reasonably pre-buy all data for a year. It also is “free” to maintain, i.e., as long as you buy some pack once every 180 days your SIM remains active. You also get a tiny amount of data with no pack active.
SoftBank?
NTT docomo (has the best nationwide coverage, along with au, for users in rural areas)
Rakuten
Specific notes:
au is by far the fastest carrier I've used in Tokyo, but it feels like a step-behind in terms of administration. You can transfer SIM cards overseas, but you need to schedule it in the My au app first. The biggest issue I've had with au is that it seemingly is impossible to update your credit card to a different one, if your name 'doesn't match' your contract name. While this might not seem like it's a big deal, none of my US credit cards, Japanese debit cards, or Japanese credit card (AmEx) were suitable to migrate my au payment to. I ended up porting one of my numbers away from au for this exact reason. au is also typically one of the most expensive.
SoftBank does not permit me to be a customer with them. I'm on the business manager visa, and apparently SoftBank doesn't seem fit to give me a contract. They reject me with a “status of residence” issue. The problem is that fundamentally, I love SoftBank. If you can get a contract with them, they have very good coverage, and an unbeatable overseas roaming plan with unlimited data use.
NTT docomo is a great carrier! I recommend you use the “ahamo” sub-brand, which is online only. ahamo approved me for use within the first four days I lived in Japan with only a 4 month residence card. NTT docomo is also the most seamless in terms of switching SIM cards overseas (“it just works”). I've seen reports of issues with their 5G service, but I have not experienced these issues. They have probably the widest theoretical coverage in the country.
Rakuten is the newest MNO. If you have a modern phone with good band support, Rakuten also has an English friendly user interface for signup and management. Rakuten also sends emails with English at the bottom, which is nice. Rakuten is also the cheapest! But it's possible to spend a lot of money with Rakuten if you add on services like voicemail and call plans.
au has an MVNO brand called povo2.0. They do have povo 1.0, but you can't sign up for it. povo 1.0 is basically just a sub-plan on au, whereas 2.0 is a full blown MVNO. povo2.0 gets the benefits of au's network, and possibly lower data priority, but with the benefit of having a lovely mobile app that allows topping up with a variety of packs. Some of their data packs and call packs are special deals or subsidized by some partners. For example, sometimes a pack includes free data with a certain company.
I was initially pretty lukewarm on the idea of using povo2.0, but the app really is good. They have data only plans that don't require identity verification, and they have data + call plans that do. The data + call package had me really skeptical at first, but when I went through the signup process I was absolutely shocked that I accidentally signed up for the calling plan because the identity verification was so easy. It was just scanning My Number Card, with no other requirements. I was very happy with it.
In terms of actual usage, I've had good luck with it everywhere except Tokyo DisneySea. With that exception, I've been pretty happy. In comparison to my long term experiment on ahamo (a plan for NTT docomo), povo2.0 has been quite good in terms of not dropping connection while on the Marunochi Line. I *have* had issues with docomo completely stopping data transmission while in some areas, where I've had to fallback on Rakuten. Because Rakuten isn't quite the best in terms of data, I would prefer to at least be able to use one other network as a fallback.
Anyways, povo2.0 gets a thumbs-up from me.
With the exception of Mobal, who really doesn't care, all of these services expect you to be a resident of Japan. Thanks to Mobile Number Portability (MNP), you can freely switch between carriers quite easily. If you're bringing an overseas phone without the Technical Conformity Mark, technically you're in unsupported territory. In-practice, modern iPhones and Android phones will work fine on domestic networks as long as they aren't carrier locked or financed in your home country. If you have an older phone, you might suffer from poor band support. Rakuten is the only carrier where this is a huge concern, because their network heavily depends on new 5G bands. If you end up in this situation, you may have poor speeds or coverage on the fallback bands.
My preference/suggestion for any new entrant into Japan is:
Rakuten Mobile to save money, best English support and experience hands down.
NTT docomo for general coverage and ease-of-management with the ahamo app.
SoftBank if they approve you, you want to use PayPay a lot, and/or you want to roam internationally a lot without excess charges.
au if you demand the fastest speeds, at the expense of cost and account-management annoyance.
I personally have contracts active on:
Rakuten Mobile
NTT docomo
povo2.0
I have used all MNOs.