Parents (and son) to visit daughter (sister) for 10 days, who is studying abroad in China - help!

We are U.S. citizens, a family of 4, 2 parents, 2 children. Our 20-year old daughter is currently in China on a student Z type, through December of this year. We (husband, wife, son) will visit her for 10 days in August, while she is in-between her summer and fall study abroad programs. We do not have official invitations, and we are not travelling with a tour group. My husband has been to China once before with our daughter in 2014, for 2 weeks. My son and I have never visited China. Our U.S. passports are all current for several more years. What type of Visa should we apply for? Is the cost of the 10-year the same as the 1 year visa, and would we be eligible for that? Do we have to go through an agency (we live in Massachusetts, and cannot travel to New York.) What documentation do we need? We will fly into Kunming, stay there for a few days, and then travel to Hangzhou for the remainder of time, and finally fly out of Shanghai.