All right.

I've played Tropico 1 back in the early 2000's and loved it.
As they are all on sale, which newer one do you advise? 3, 4 or 5?

Which one is the favorite of the community?

T4+CompleteDLC +LockNotMod (T5 is not the most fun..)
( and T-Reloaded, for the musics of T1, and for T2-PirateCove if you like the pirates. )

First thing to bear in mind is that the new games are easier than the original. I have to play Tropico 4 with all of the sliders set to the most difficult settings and a score multiplier of over 200% just to make it feel like a challenge, and I still never lose. So while 4 does introduce the most new content and is a worthwhile game for that alone, it doesn't have the same sense of paranoia that a few bad choices could destabilize your island that the original provided.

Tropico 3 is basically a modernization of 1 in a 3D engine. It doesn't have as much new content as 4 but is more balanced. It's a little easier than 1 but a big part of that is the improvements made to the road system, which makes your tropicans more efficient overall and enables you to build remote villages and outposts rather than a large sprawl.

Tropico 2 is the odd man out in the series and really doesn't have a lot in common than the others. It's considered the weakest of the bunch but still worth checking out for being the best (and only?) pirate themed city simulator on the market.

The original is still my favourite, but I occasionally play the newer games. 3 and especially 4 de-emphasize the importance of your Tropicans and focus on budget and infrastructure, so they're more in the way of traditional city builders If you want to focus on the social aspects of juggling political factions and and keeping in office no matter what, then stick with the original.

I like the second part a lot. Pirate setting is really cool, humour is great and I still keep the soundtrack on my mobile phone. Management aspect is similar to this from the Settlers i.e. 4 iron ore = 2 ingots = 1 sword. Sometimes sea battle randomness might screw you badly, but that's just an additional challenge.

Many people dislike it, because there is very little Tropico in there, but I really think it is worth trying.

I'd recommend to try 1st, 2nd and 5th.
3rd, 4th and 5th are way to similar. It is true that 5th does not have a DLC pack yet here on GOG.com, but those will eventually arrive here as well. Until then, you can enjoy first two parts.