My husband and I are independent and have never been with a missions organization. We serve with a medium-sized South African ministry, so there is structure and accountability where we live and work, but we are on our own for the logistics of being overseas, raising support, etc. On the pro-side, we have found solutions for visas, health insurance, how to allocate our time, setting a budget, how frequently to visit the U.S., etc., that suit our individual situation. We have had to do some work in this regard, but we don't have to follow policies that don't suit us. For example, we have very reasonably priced health insurance through a South African company that includes some coverage for our trips overseas, where I believe many agencies would require us to purchase international travel insurance through a U.S. company, which would probably be more expensive and provide less coverage.
On the con-side, we have to find our own way in terms of fundraising, understanding how to work cross-culturally, self-care, and other things for which an agency might provide helpful training and support. Our two main sending churches in the U.S. and ministries like Thrive are helpful in some of these areas, but in others we are on our own and it shows!
The bottom line for us is that we feel called to this specific assignment and are happy to be responsible to our ministry in South Africa without having to deal with another organization with different priorities, but there are some costs to that. I hope you get a lot of input from other people, because everyone has a different story and you have a lot of factors to weigh to come to the right decision for you!