[Kalimac]

The effects could go back even further than that - there's that bit in "The Shadow of the Past" where Gandalf says something to the effect of "You may be sure that Bilbo took so little lasting harm from the Ring because he began his ownership of it so, with Pity." There's a pretty serious implication in there that if Bilbo had killed Gollum, he would have been replicating Gollum's murder of Deagol, with all the attendant complications that that brought about. Gollum killed Deagol in cold blood - his first act as owner/potential owner of the Ring, and Gandalf hints that the first act of every new owner will color his subsequent life greatly - set the tone, so to speak. If Bilbo had killed Gollum in cold blood - and that's what it would have been, regardless of Gollum's intentions, since Gollum could not see him - I don't believe he would have been able to forget it; Bilbo was too honorable to tell himself for long that it was the only thing he could have done. He would have been haunted by remorse and the Ring would have taken him over much more quickly - he would have had to compensate for his guilt by loving and justifying his right to the Ring, the same as Gollum did.

In which case, he might not have even stayed in Bag End long on his return; he would have wanted to be alone with the Ring only, and the malice with which he had begun his ownership would doubtless make him very unpopular among all the hobbits, and for good reason. Gandalf might have been able to stop him, or figure out what was happening before Bilbo went wandering off somewhere far away - my guess is that if he had, he would have tried to get Bilbo to Rivendell double quick and then try to persuade him to give up the Ring. If he wouldn't give it up - they may have had to take it from him, with all the horrible effects this would have had on poor Bilbo. From all this, rumor would probably have Sauron about then that the Ring was found, and a totally different fellowship would have been formed, but whether they would succeed or not would have been entirely unrelated to hobbits, who would probably have suffered all the earlier at the hands of Saruman, as creatures with a rich land and few defenses, but with no Scouring afterwards.

It's implied that it didn't take Gollum very long to succumb and be driven away from his village once he had the Ring - a few years at most. It probably would have been the same for Bilbo. In that case, the Ring would have left Hobbiton before Frodo was born, or while he was a toddler, so he would never have been involved and possibly never even met Sam (who without Bilbo and Frodo around would probably have stayed at home all his life and become a second edition of the Gaffer). Merry and Pippin would probably have been much the same as they were at the beginning, but of course with Saruman in the background who knows how long their fun would have lasted.