I have the original Tropic Gold, I played it back when it was released, it was good but not great.
Is Tropico 3 better or worse than that?
Are time limits skippable for random maps games?

It's about the same as Tropico, with some annoyances fixed (for example, your people seem to be somewhat smarter, or the introduction of the garage to grant a car to anyone who needs it), plus some nice features (such as, planning your election campaign speech, which you can actually listen to on the in-game Tropico radio station). Mostly, though, it's the same game with improved graphics (which are actually exceptionally good, mostly due to the attention to details; and this is something coming from someone who generally doesn't care much about graphics in a game).
What do you mean by skipping time limits? When I reached the time limit for my game, I got my evaluation, and then could continue my game.

It's worth it. Given that Tropico 4 won't be out for a while this will be good enough.

It's the best one yet. Especially thanks to the inclusion of roads. That hasn't stopped it being sold very cheap though so I certainly wouldn't recommend paying too much for it for that reason alone.

It's on sale right now actually.
$6 on direct 2 drive. http://www.direct2drive.com/promos/d2d-turns-6/
And yes, it seems the game goes on sale regularly ( I bought mine for $7.5 on steam a couple of months ago)

Or rather 6 [insert your currency here] thanks to the wonders of D2D's non-existent currency conversion skills.

It's only better with it's expansion Absolute Power.

That's if you can actually purchase it at checkout.

Ah yes, D2D's miraculous policy of NO GAMES FOR YOU! The Soup Nazi of the internet. Which ultimately is why I've never bought anything from them, nor ever will - simply because I can't.

Sure! It's awesome, i wasn't too impressed with the previous Tropico titles. But the third one made my day... and night.. repeat until completion. The expansion is also cool, but is more 'weird objective' oriented, as in, obey monkeys, or decipher transmissions from outer space, they are hard, and ridiculous, but real fun if You dig T3, and know how to play the game well. The only bad thing about it, is that it gets pretty easy with time, when You learn what and when to build, You can just sit back, sip colitas, have a cigar and watch the game play itself. But it's worth every penny.;)

Well, you see D2D isn't actually a digital distribution outlet. For whatever reasons they have they're merely pretending to be.
Unfortunately for them they have to occasionally let people buy things through the store in order to maintain this pretence. How these select few are chosen is known only to D2D. But clearly we're not among the chosen.

I have bought several games from D2D over the last year or so. No problems yet.
Now, regarding the game, thank you all for the suggestions. I think I will buy it.
As for the expansion pack, I have zero interest in scenarios so I guess I won't need it any time soon. Thank you for the info.
Three gameplay questions.
1)Do roads have to "touch" each building to service it?
2)When I build a farm, how many plots of land does it use for farming and does it automatically cut trees etc?
3)Buildings like police stations, schools etc, do they work for the whole island or just for a smaller section of the island?

1. No, but the closer the better. If you place a building and the roads aren't close enough then you'll be notified about that fairly quickly. Roads are extremely cheap things to place so it's usually not a problem. Usually it's wise to lay down a rudimentary road layout early on to guide your development.
2. Trees usually aren't a problem. Crops are either planted in their shade or the tree is removed. As for the number of crops, that seems to be somewhat governed by the number of people working on that farm. But it's usually wise to set aside an area at least twice the size of the farm itself (all green for the crop you're planting).
3. Police stations are connected directly to your roads and thus can send out car patrols. Their influence starts to wane the further away they are from the scene of the crime. But their reach is generally island-wide.
As for schools, building a garage near them along with some cheap tenements or bunkhouses (enacting social security helps too) is all you generally need. But having them nearer population centres seems to bolster attendance.
EDIT: a few more notes.
1. You'll need to place down garages in every area you're developing. Naturally these need to be connected directly to the roads. The more developed an area the more garages you'll need there. When developing a new area, place garages down first and make sure it's set to high priority.
Even send out Presidenté to the site to speed up construction. This will give your construction workers means of getting back quickly and thus back out building again all the sooner. Otherwise you'll have all your workers wandering back on foot.
2. When it comes to farms and ranches, don't actually place the building on the greenest area, but beside it. Mines and oil wells on the other hand you want right on top of the resource.

Yes