Query regarding new job possibility and citizen’s insurance.

Recently I’ve gotten the opportunity to work at an English teaching school and was very excited about the prospect of starting. However, due to the contract stipulating I will be working 29.5 hours per week, I will have to use the citizens insurance (市民保険/国民保険, I’m not sure which it is, it was stated in English). So I will have to pay extra for my health insurance and pension. Is this normal? I at my current job I have 社会保険 so pay less but my wife got a little suspicious so I wanted to check here. The people at the job said after 1-2 years I can move up to 30+ hours but that will be negotiated in future.

I guess my questions are, do I have anything to worry about? Is this normal? Do any of you have to do this and how do you get by?

by Shinosei