Nunu works as a support and actually was where I started using him. Punch minions without killing them to stack his passive, then throw snowballs or buff your teammate, eat a minion when Relic Shield passive is up for massive sustain. I do recommend taking him into the jungle though as he's better there.
As for cheap and effective ADCs, I recommend Tristana or Corki (both Yordles, same race as Teemo), or for more difficult ones, Twitch and Draven.
Easy support would be someone like Sona (Attack with Q by getting close, heal your teammate when needed, know when to use your ult) or if you want a more skillshot and straightforward champ, Blitzcrank. Blitz is like Thresh in that he's got a pretty defined role: Grab, knock up, possibly ult, and exhaust so your ADC can do damage to them, but he lacks the versatility Thresh has.
Blitz does well with some mobility and tank items (I tend to go Face of the Mountain, Sightstone, Mobility Boots, Righteous Glory, Mikael's Crucible or Locket of the Iron Solari, and possibly Iceborn Gauntlet if we're ahead)
I like doing full AP Sona, (Frost Queen's Claim, Sightstone, Either Mobility or CDR boots Only support items there, then situational AP items like Abyssal Scepter, Athene's Grail, possibly Void Staff/Luden's/Rabadon's) but not many people agree that it's smart, even though it's fun and works.