When it comes to burying the threads, I've very recently converted to using the "lasso" method. I think there's a YouTube video on it somewhere out there. It makes it a lot quicker because you don't have to thread the needle for every thread you have to bury!

I use a John James Easy Thread needle for this and for broken threads. It's like using a lasso method but much easier and can be used with even a short piece of thread if you insert it most of the way in before "threading" it.