Nobody is answering your questions. I'll try.
Judo and BJJ are both fine for beginners - if you find the right school.
Check out the schools in your area. Ask the BJJ schools how much they work takedowns. If you can find a BJJ school that regularly drills takedowns and judo throws, you are golden. This isn't that common, though.
You can always post a link to the school's website in this thread and ask people for advice, too.
Check the instructors' credentials (who promoted them,) and the students' competition results. I love BJJ and think it is the greatest thing ever. But even I would prefer to see a beginner go to a good judo school where they will thrive over a crappy BJJ school where they will quit after a month. Also, if money is a factor, you will find judo much,much more affordable.
Pretty much everyone will offer you a free class. So try the places out and see how you like the people. That's a really important consideration
BJJ grades:
white
blue
purple
brown
black
Judo grades:
white
yellow
orange
green
blue
brown
black
Both arts have extra belts for kids and honorific belts past black.
I think in both, there is no formal grading system. In judo, there are some kata and stuff certain instructors want - but I believe in both arts you can be promoted solely on competition results.