First Ranger.
I've two thoughts on Benjen joining the Night's Watch. First, the Starks are inexorably linked to the NW. Houses Tully, Baratheon, Lannister, Martell, Tyrell, Greyjoy, and Arryn do not view the continued success of the NW of any real concern to their own power bases. Remember the laughter that Tyrion's japes at Ser Alliser's embassy to the Iron Throne? The entire realm views the NW at best, as a dumping ground for their hardened criminals, and at worst they see the NW as border guards for House Stark. One of House Starks philosophies is to keep the leadership of the NW friendly to the interests and safety of the North. I think Benjen took the black to be the next generation of Stark friendly leadership in the NW.
The other thought I have is that in the immediate aftermath of Robert's Rebellion, the Starks decided to hedge their bets. Eddard broke three hundred years of Targaryen dynastic rule through blood and vengeance. Was he positive the new order ushered in by himself, Jon Arryn and Robert Baratheon would last? By returning to Winterfell, either Eddard felt that Robert was secure on the throne or else he was preparing against the eventual backlash by preparing the North. Or maybe he was still too mad at Robert to stay by his side.
Eddard could have easily stayed and served on Robert's Small Council. Sure, Jon was Hand, but Eddard could easily have been named Master of Laws... I've no doubt he'd have been better than Renly. Eddard could have filled other positions as well, Master of Ships, Master of Coin, Commander of the City Watch... and Eddard could even have undertaken the mission to seek out Ser Willem Darry and apprehend Viserys and Daenerys. (Eddard would not have killed them, this would have been his chance to make sure they were put beyond the reach of Robert's knives.) And all the while that Eddard would've been serving in King's Landing, Benjen could have been Warden of the North.
Eddard dreamed of repopulating the Gift. Well, who better than Benjen to lead this effort? But Eddard did not stay in KL and he did not give lands and title to Benjen... Maybe he wanted Benjen to be free from the mess that Robert's reign might bring.
But after taking his vows, Benjen could not legally marry and pass on his name to a son. So what is the advantage of Benjen taking the black? Is just to live a few years longer lamenting the wreck of his house, just like Maester Aemon?
The thing that Benjen could do in complete safety from the Wall would be to watch and protect Jon Snow. IF there came a time when the Starks would be annihilated, then Benjen could bring forth Jon to keep their blood alive. We know the NW does not permit members to ever leave, but IF Jon was proved by Benjen to be the only legitimate and legal heir of Aegon the Conqueror and Aerys II through Crown Prince Rhaegar, then I think the High Septon, the Conclave, and many of the assembled lords of the realm would clamor for an immediate exemption to the NW's laws. They could claim that a Targaryen is not bound by any oaths that a Snow made.
That all seems rather preposterous to me to be a valid reason for Benjen to join the Night's Watch. Like I said, I favor the continued rapport of the northmen and the crows.