Well, let me be the 1st to say "you should have called a pro". Be prepared to hear that about a dozen more times.
Ok, enough sarcasm... I'd go with mastic (aka pooky). Silicone is somewhat messy (at least when I put it on), some of it can really stink, and it's somewhat time consuming to put on.
Mastic gets smeared on with a cheap paint brush, doesn't really smell and cleans up with water.
About the only time I use caulking to seal duct is if it's going to be exposed in some fancy building (mostly commercial). If it's in a residential setup and exposed, I still pooky.