We should have done this years ago, but I suspect, like many, we were nervous of sending these precious memories away. What if they were lost?
In the end, we used a company called EachMoment who were excellent. At every stage of the process we were kept informed. The resulting DVDs came back with the original tapes about 2 weeks later. Thankfully, even after all these years, they copied fine.
I would have no hesitation using them again.