As regards getting part time work, i haven't seen or heard of it being a big problem. As long as if you don't over work the required hours you can only do (work hours are restricted when you are in education) then i don't think it's going to be a problem.

As regards work, when you are on a student visa/College Visa etc you are mostly unrestricted in types of work you can get, but realistically it will come down to:
- Teaching English
- Hospitality Work (Bar/Cafe/Resturant work)
- Working at your college (few hours here and there)

It will all depend on the job though and the people who want to hire you. What will hold you back getting a wider variety of jobs will be your level of Japanese.

Also regarding your point on cost and also the permanent residency thing...

Initially it will come down to the University you go to but the cost of studying in Japan is very expensive, even taking the factor of working into account (i thought about doing this myself). Depending on the college it will cost from 40,000-80,000 euros (probably more in dollars) to do a 4 year bachelors degree in tuition fees alone. In my own country and with the benefits of government paid education, i can do the same 4 year bachelors degree for at least 6,000 euros (i can get it even free if i qualify for a grant). You may also have to prove to Immigration that you have substantial savings in account before being accepted for a visa.

You are going to have to really weigh up your options if doing a bachelors degree in Japan will actually be worth the financial risk. I know doing it would be awesome (i thought it would be) but when it comes to cost the reality hits home.

Regarding the Permanent residency, it's more about quality vs quantity. Your time spent of what you do in Japan is very important for Japanese Immigration in deciding permanent residency visas.

Best of luck with it though, i really recommend doing more reading regarding everything said before deciding anything. I would have loved to do it myself but realistically for me it wouldn't have been affordable. If it works out being viable for you then i truely wish you the best with it!