A 5D Mk III and 6D have different strengths. The 6D is said to be a little better in low light while the 5D Mk III has better auto-focus. Usually the 6D is less expensive to purchase. There are lots of comparison tools on the net.
Auto-focus was a major upgrade from 5D Mk II to Mk III.
The 50D is in the middle of a line of great bodies starting with the 10D and progressing through the 70D. Unlike the 6D, 5D and 1D variations, you can use EF-S lenses with the 50D. You can also use all the full frame lenses, and a wide range of third party lenses, too.
Lens choice varies based on lots of factors. Longer lenses compress the scene which keeps noses smaller looking, but if you are shooting an open event like a Christening or Baptism, or a Bar Mitzvah or Bat Mitzvah, where all the participants are apt to have cell phone cameras or P&S, a short lens is a good choice so you can get as close as all of them, otherwise you will be shooting their backs. If you are using lighting, fast lenses are not so important. If you are using ambient light in a church or house, a fast lens may work better at the expense of depth of field.
All of this has been extremely generalized. There is a lot of gear, a lot of science, and many methods available to achieve similar results. Classes and practice in the field are good ways to sort out what works for you. But, if you have specific questions, don’t hesitate to ask, here, as well.