How important are fruits & veggies?
They aren't, in my opinion. I believe that dogs are carnivores, so I never feed them, except sometimes as treats. Some may disagree, but I think there's more evidence and proof on the carnivore side and more observations on the omnivore side.

I am planning to feed them daily, but, have also read that you don't need to.
You can if you want to, but don't let them take over the diet. I would not feed more than a tablespoon a day, or around 5% of the diet.

Also, should veggies be bought fresh on a regular basis, or can I put it through the food processor and freeze it in portions?
You can definetly freeze them. I think that would be easiest

Eggshells. I have tried, occasionally, putting an egg(with shells) over Jasper's food. He loves egg, but will spit out the shell. Is it fine to give eggs without the shell, or should I just crush it up?
Mandy is the same way. I stab it with a fork a few times to break it up and she gets some of it, but still leaves some. Sometimes I don't feel like dirtying up a fork, so I throw the egg in the bowl, slightly cracking it, hoping she'll eat it in order to get the goodies out, but she never does. She finds her way around the darned thing. I don't see a point in getting out a blender to add it, all it is is calcium, and there is plenty of that in bones.

Last one I've read, over and over, that you dont need to feed a balanced meal everyday. Is this true?
Yep, this is true! Balance over time! If they needed a balanced diet every day that means you'd be feeding a lot of different cuts of meat, and that just isn't neccessary. It's okay if you are low on money and can only afford chicken for a few weeks. Balance over time, not every day!

Does this mean no veggies everyday?
Yep, just feed them whenever it's convenient.

That somedays I can feed raw meat with less nutrition/calcium(such as leg quarters, etc.)?
Chicken doesn't have less nutrition than another cut of meat, but rather provides different nutrition.

I would also love if someone could list the best staples for a raw diet, and other things fed for variety.
I think it's best to have at least four sources of meat as the main staples. These are usually chicken, pork, turkey, and beef, because they are the most readily available. If you choose four different meats, so be it.

The best thing to start with?
Chicken. It's cheap, it's bland, and it rarely causes problems. Sometimes, though, dogs who are finicky don't like the taste of chicken at first, in which case I would try pork or turkey. Don't start out with beef, the bones aren't edible and you need to start out with bones.