Vets are like any other professionals, some are really good, some are not so great. I would contact your practice and ask them when you pup will be safe to take out again - in view of the antibiotics as well as the vax - also sometimes having antibiotics at the same time can make the vax less effective.
Also when the vet says not to take the pup for a walk do they really mean not to take him to areas where other dogs might be?
Here is a link to a free down load of Dr Ian Dunbar's 'After you get your puppy'
http://www.dogstardaily.com/files/AFTER%20You%20Get%20Your%20Puppy.pdf
Which talks about all the socialisation your puppy will benefit from in helping turn him into a dog that will be a pleasure to be around.
Also do not think of obedience class as something to start at a certain age. Think of it more that you are teaching him manners, and 'right from wrong' in your world - eg to a dog the whole world is a chew toy. To you his toys are chew toys and everything else is off limits. Again the download I've linked will help you work through these things.
The same with play if you run with Basil it is perfectly normal for him to want to grab you trousers/legs, you need to show him this is not appropriate play with a human. Have a toy, like the ball, or a soft toy/rope tug that you substitute for your trousers. That way the game continues. If he insists on attacking your legs. Just stand up and walk away game over. He'll soon learn which is the most rewarding - what keeps the game going.
We run puppy classes which if the puppy owners want to keep training their dogs (and most do) they go on to our more formal class after they graduate from the puppy socialisation course as the pups have learnt how to concentrate and work for short periods in an environment with other dogs and are ready for more focussed training.
Good luck with your little guy, he certainly is a cutie-pie!