Bit shocked to discover that our new puppy who only arrived on Saturday appears to have fleas

. The breeder had said he'd been frontlined which I thought was meant to stop fleas? But we don't have any other pets and he hasn't been anywhere/come into contact with any other animals since we got him so I don't see how else he could have picked them up.
I rushed out to PAH this afternoon to arm myself for the war - I've given him Johnsons 4 fleas tablet, flea combed him (and drowned all the suckers I found). I've hoovered and Indorex-ed all the areas that he's been in, including the car. Oh and I've nit combed the kids and me - just OH to do when he gets home

Should I be doing anything else? Will this be enough?
Also, the Johnsons stuff said to give him a tablet any time I saw some fleas (just not more than one tablet a day) - does that mean I'm supposed to keep giving the tablets to him until they're completely gone?
Is there anything I can do to stop him getting fleas again?
Sorry for so many questions but the thought of it has literally been making my skin crawl all afternoon

Thanks
E x