Aeon Bank has been mentioned a few times as a decent option for mortgages.
I recently opened a bank account with them and then added an investment account.
The bank manager told me they are aiming at beginners really, but if you live near an Aeon or use their shops or credit card a lot, it may be worth considering.
Plus points
1 I was able to open the investment account all online with photos of my ID, which is a slight improvement on those securities firms which insist on the paper version for non-Japanese.
2 Phone app seems easy enough to use. Online account is also fine. Less cluttered than some others.
3 Some decent, low-cost funds, notably iFree (0.2475%)
4 They rank you as a bank customer depending on what services you use, similar to the way Sony Bank and Shinsei operate. So, having some money in the investment account can bump up your level and get you additional free furikomis, it seems.
Minus points
1 No eMaxis Slim so even the iFree funds are a bit more expensive.
2 No ability to buy individual stocks
Not sure if anyone else has used them for investments. Not a replacement for Monex, SBI, Rakuten perhaps, but could be useful for some people.