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I was thinking about playing as a Ranger. Someone who uses light armor, archery, one-handed, destruction magic, restoration magic, alchemy (I find potions really come in handy), sneak, lockpicking. I don't like playing as a thief or assassin so I decided to try this. I was thinking either Khajiit or Argonian, what would be the best? Argonians are good at healing and have an all terrain advantage because of their water breathing ability, but have no combat bonuses while the khajiit have that really handy night eye (or whatever it is called) which helps me see in dark places and a wicked claws ability while unarmed, but no armor bonuses. Anything else I should put skills in?

I Agree with shi-sen about the skill modifiers being kind of moot. I would reccomend playing Argonian in this case as the Kajjit night eye is basically the same as adjusting the screen brightness in the options menu (at least it was in Oblivion). It also sounds like your hands will be too busy holding weapons or casting spells to use the increased hand to hand damage.

Then Again, I pretty much always play Argonian so when I play anything else I notice how much racial abilities like waterbreathing and disease resistance impact on how I play.