All good advice above, The Henderson chart is the best one-pager that exists out there that I've seen. I have also referred to it a lot.
First things first, what are your goals for your flock? Egg production? Meat? Dual purpose? Breeding and selling hatching eggs or chicks?
Why do you want a rooster? To protect the flock? Or do you want to breed? If so, breeding to sell or just to increase your flock at lower cost than buying more chicks? Keep in mind more people are interested in buying pure-breds than barnyard mixes.
These are all questions (and I'm sure there are more) you should consider before deciding on which breeds, to make sure you can accomplish your goals. If you have already, good for you!
Most breeds get along together just fine. Size is an issue sometimes, as mentioned. I have Lf and bantams all happily co-existing.
'Recommended' sex ratio is one roo to every 7-10 hens. While you might get away with more while they're young cockerals, at some point, there will not be enough girls to go 'round, in their tiny minds, anyway. If you're going to get 7 birds, I'd get 1 boy and 6 girls.
BOs are usually gentle and have a tendency to go broody. Broody is great if you want to raise chicks, not so much if you want eggs. They're a pretty good layer when they're not broody.
EEs aren't known as a particularly broody breed and give you green eggs, usually. They lay pretty well and their eggs get pretty big.
I'm not sure how the single silkie fits in...as a pet or ornament? They're not prolific layers although they do like to go broody and hatch eggs. They can't cover the eggs a BO could, though.
My favorite boy was a Buff Brahma. He was a big gentle giant as a cockeral, quite striking looking, and seemed very concerned with the pullets' welfare. He didn't have the attitude my BluCM cockeral did. I can't keep roosters so don't know how he turned out as an adult. I wish I could have kept him, just as a flock protector.
Good luck!