I've never played any of these games but I would like to give the series a try.

What's the best entry point for a new player? Older games don't scare me!

Settlers 2 Gold. It's still arguably the best of the series and has aged pretty well.

3 and 4 introduce a new engine, changed some of the mechanics, and though I enjoyed them they did move away from the formula which in my opinion made S2 great.

If you can get your hands on Settlers 1 (it's not being sold anywhere; so either an original disc from somewhere, ebay perhaps, or an abandonware site), from what I know it's a simpler version of Settlers 2. I don't think it had a single player campaign.