Visiting China to stay with my wife's family, wanting to stay 6 months, which type would allow this?

You can try to apply for a family visit visa L type with invitation letter from your wife and your marriage certificate. Copies of her Chinese ID card and Residence Certificate are also required. Also, you can enter with a tourist visa, then change it into a family visit visa after entry at her local PSB. For mroe information, you can refer to https://www.travelchinaguide.com/embassy/visa/family-visit-permit.htm