I would certainly not keep the pup at home for the first few weeks - imo it is a crucial time to introduce your pup to the world. Just make sure you have plenty of time as everyone will want to stop you and talk to your pup!
I took Coco out and about with me from day 1 (well probably day 2 actually
) She went in the car every day, I carried her around and took her into town to get used to traffic, people, noises, smells etc etc. I am sure this is the reason she is totally fearless - nothing fazes her (well hot air balloons drive her bonkers but otherwise...)
There is a list in the back of the Gwen Bailey book The Perfect Puppy of suggested things to introduce your pup to in the early days. I think the first few weeks and months are crucial for this. The two things I totally failed to do right were getting her used to being left behind - I was so keen to socialise her I never left her at home, and I didn't groom her enough early on so when I needed to start grooming her later on she was not very keen or cooperative
Oh, well, you live and learn. Still, I think I would rather have an over socialised pup than a timid one.
I took her to a puppy party at my vets in the first week - they hold one every month for all the new pups and it was run by the same person that did the puppy training classes we went to. I think a lot of vets do these so you could ask yours about this. Coco then started puppy class at about 10 weeks after her first vac and before her second one. At that age, classes are more about socialisation than learning obedience but it was fun and she did learn how to play nicely with other pups and the basics - or more importantly I learned the basics!!
Your vet will advise you when it is safe to take the pup out for a proper walk - I think it is usually a week after the second vac though.
Good luck with your search - I am sure you will find your perfect playmate soon