Ditto not choosing Cohen....
As far as modern goes...I love Ezra and we almost used it as a first name but its one of our ds's middles. Also, Levi (used as a middle), Seth, Micah (too similar to Mike/Michael for my personal taste but its a neat name), Jonah (very popular where I live but I love the sound of it), Ari, Judah, Gideon, Reuben, Isaac....brain freeze thinking of more.
Unusual, well, again, we chose Elihu. Helps that I'm a Phish head so it doubles for anybody in that crowd. ;) Also Lemuel but since I read the Red Tent I cannot get over the "character" of Lemuel.
Elihu, up on Leemor's bed" when I read it. I can't say I am a current Phish head, but spent a significant part of my college years and a bit beyond with the Phish head crowd and going to shows. My SO is still a HUGE Phish head. :)
I really like the name Ari.
Noam, Ari, Zev, Tzvi, Gilad, Aryeh for Jewish but not strongly Biblical.
Gideon, Naphtali, Ephraim, Ezra, Mordecai, Malachi, Phineas, Zebulon, Hezekiah, Azaria - the semi-quirky Biblical names I like.
Actually I don't know if you'd count Aharon or Reuven, etc. as uncommon or not. Aaron and Reuben are mainstream, but are those? Zevulun probably didn't get much weirder than Zebulon is anyway. I'm fond of Gavriel.
Jethro I've heard called hickster, Yitro is definitely uncommon, I like both.
Also not Jewish, but I cannot get over Avi. I've loved it for a long long time.