I got Tropico 1-3 in Steam. Should I play them in order?

Nope, there's no real reason to play them in any particular order. Tropico 3 is more or less a remake of Tropico 1, albeit with some different scenarios. Tropico 2 has a completely different focus, (Pirates!) so it doesn't matter when you play it.

There's really no plot or story or anything in particular that can be spoiled by playing them out of order. Tropico 3's really the most modern of the bunch, so I'd suggest just sticking with that and ignoring the other two, unless you're interested in them for historical reasons.

I'd almost say it's like playing one of the earlier SimCity or Civilization games when you have the latest one available - they're a bit different, (Tropico 2 especially...) but by and large they're just iterations of the same formula.