My puppy had a collar that adjusted 13-20 inches. She wore it at about 13.5/14 inches at 8 weeks old.
I like a harness, slip leash can tighten too much on their neck.
For fish oil we personally use Grizzly Salmon oil (boutique stores/amazon/online), its a pump that you just squirt stuff on your dogs food, but other people will have good input about capsules if you prefer those!