I've just gone through the house buying process myself, so I can try and give my opinion for some, but not all of your questions.
First off though, one of the others posters said you would need a guarantor. This is not true. Even for Japanese people, most banks nowadays prefer you to pay for a "guarantee fee", which covers the bank in case you default. The banks consider a guarantor company much more reliable than an individual guarantor. I got my mortgage this way, and all the banks I talked to were the same. Nobody asked me if I had a personal guarantor.
- Should I buy a new home, or buy a used one and rebuild? What are the pros and cons of each, in terms of taxes or other expenses?
New builds are either custom built or pre-built (aka tateuri). Obviously, if building your own house, the big pro is customization, the con is the higher cost.
If you buy used, you want to look for a custom built house, rather than a tateuri (tateuri's are the ones that give Japanese homes the reputation for shoddiness). There are plenty of used custom-built homes out there, where the original owner put a lot of care (and money) into ensuring it was built to a high-quality standard. This is where deals can be had. When you find one with potential, you will need to be willing to pay for a professional inspection, in order to assess the condition and to understand what maintenance work needs to be done. The inspection will cost you 10-12man-yen, and you will need to be willing to part with that money and walk away if the inspector finds too many issues. On the flip side, no used house will be perfect, there will always be some issues, and you can those as negotiation cards to get a better price.
There are tax breaks to be had on the mortgage for up to ten years. Most new builds will qualify, while used builds may qualify but will need to meet certain age (within 25yrs) and quality conditions. The tax break works out to a max of about 400man spread over 10 yrs. While this is not an insignificant amount, in my opinion it is not large enough to automatically disqualify older properties that are not eligible... because the premium you pay for a new build will often be much more than 400man.
As for the land, it's the same as anywhere else, location location location. Pick what's best for you.
What bank(s) would you recommend for the loan and why?
The bank you should go with is the bank that offers you the best deal. That's it. Your real estate agent can act as a go-between as you do several pre-approval applications. I did about 6-7. Apply for the Flat 35 as well. Make all the applications the same so you can compare apples to apples, and then take the best deal, considering interest rates and other fees, as well as options such as insurance.
One of the banks I applied for was Shinsei, because they can do everything in English. I found, however, their interest rates were not competitive compared with other banks, and they were also the only bank that declined to lend me the full amount I was asking for, so I went elsewhere.
- If I decide to build a home, how do I find a company to design and build it?
Two primary ways. If you want the bigger "name" places, visit your local 住宅展示場, where several house makers will all have beautiful model homes set up in the same area, and you can freely walk in and check them out. The other way is to find an independent 工務店 to build your house for you. These you need to find yourself, and as such you will have to do your own research about their reputation, but the price will be much better.
Note that many of the big house makers often end up subcontracting the build out to a smaller 工務店 anyway... so the same guys might build yoru house either way, but what you pay for with the big companies is the "reputation", and the aftersales care that comes with a big name. Different people value that in different ways.
One final note, on the issue of manshon vs. house. For comparison's sake, assuming you get a 100% mortgage, fixed interest over 35 yrs, and assuming 50,000yen in fees (kanri-hi, shuuzentsumitatke-kin, and parking) for your typical manshon in the Tokyo/Yokohama area, those added fees are the equivalent to almost 2,000man in the house price. In other words,
the annual cost of the mortgage + fees on a 4,000man manshon will be the same as what you pay on the mortgage of a 6,000man-yen house. For me, as the latter choice allows you to own land, and the fact that I could buy much more house for 6,000man yen than for 4,000man in the manshon market, the choice was obvious.