Who would have fallen?

[the phantom]

Sam seems to be unaffected by the Ring's power.

That might be because the Ring didn't care about tempting him. The Ring was content to work on Frodo and Gollum. The Ring wants the quickest way back to its master, and it knew that Sam was a sturdy little fellow that It would have to work on a bit to get him under control. It wasn't worth the effort.

Boromir, on the other hand...

If Boromir had taken the Ring it would've gotten back into Sauron's hands fairly quickly, because Boromir fully intended on using it against Sauron. There's no quicker way for Sauron to get the Ring back than for someone to stand up and say "I have your Ring and I'm going to defeat you!"

The Ring would try and tempt people who had that sort of attitude- people who would use the Ring.

Sam and Frodo (probably hobbits in general) were not the type to try and use the Ring to contest with Sauron. When Sam had the Ring and the Ring tempted him to challenge Sauron, Sam knew he wasn't powerful enough. Here are his thoughts from ROTK when the Ring was in his possession-

He felt that he had from now on only two choices: to forbear the Ring, though it would torment him; or to claim it, and challenge the Power that sat in its dark hold... Wild fantasies arose in his mind; and he saw Samwise the Strong, Hero of the Age, striding with a flaming sword across the darkened land, and armies flocking to his call as he marched to the overthrow of Barad-dur... but also deep down in him lived still unconquered his plain hobbit-sense: he knew in the core of his heart that he was not large enough...

Notice two things-
1) Sam's thoughts are much like Galadriel and Boromir's when they are tempted. They all see themselves overthrowing Sauron. That proves that the Ring can have the same sort of effect on those surrounding the bearer as it does on the actual bearer.
2) When it comes down to it, Sam doesn't think he is capable, therefore he is unlikely to make the attempt. Galadriel and Boromir on the other hand, because of their pride and power, seemed to believe that they were capable, and I believe that is why they were influenced second-hand by the Ring where as Sam really wasn't.

I think its completely possible that the Ring picks its targets, and tries to work on certain individuals. If Boromir wasn't there, who would the Ring have gone to work on?

When you consider Sam's temptation and his unconquered "hobbit sense", it seems unlikely that a hobbit would be the first to fall.

A hobbit (Frodo) took the Ring farther than anyone else could, a hobbit (Bilbo) gave the Ring up, and a hobbit (Sam) supported the Ring bearer to the end. Given the evidence, I think that Merry and Pippin would have fared as well as anyone.