I have a craving to play a strategy game, something unusual for me. I'm thinking either Tropico or Empire Earth, but I am open to suggestions. Any advice would be greatly appreciated, and please ensure the game is available on GOG. Thanks!
PS I own HOMM3, would prefer RTS

Both of your suggestions are quite nice, and very solid representatives from their categories. EE is a very well made standard, base-building RTS with a surprisingly challenging AI, and Tropico gives you quite a number of possibilities to govern your island.
Staying with the RTS line, I can also advise Seven Kingdoms/SK2 to your attention; those games have a bit of everything: combat, research, espionage, trade, diplomacy, you name it.
And if you'll take a TBS suggestion: take a look at Conquest of the New World. It's a sadly overlooked gem in my opinion, where you have to build a colony in the New World while paying attention to a number of factors (such as your relation with the Mother Country, the presence of the natives, activity of other players, trying to settle around bonus-giving natural resources...).

Also to keep in mind, the original 3 Command and Conquer games are freeware now if you like those, although the c&c site appears to be down currently.

The Earth trilogy is very good RTS, though tough at times.
More focused that
Empire Earth, both games available here are very good, but very broad.
Evil Genius is good.
Ground Control games are very good too.
Haegemonia is RTS in space, good.
Perimeter is the newest RTS I think available.
Sacrifice is RTS but with action elements (closest game to Ground Control)
Tropicoo Reloaded is worth the money, but I never managed to play more than an hour before getting bored with it.

Empire Earth II if you want more modern, and more likely to run on Windows 7/Vista (I know EE1 has issues).
You mentioned "unusual". It doesn't get much more unusual than Perimeter... it's really tough, too, it's a super fun game, especially if you're an experienced RTS player.

Spellforce Platinum is a very good mix of RPG and RTS.

Well it's not on GOG (yet...I'm hoping it's coming!) but it's a great 3D RTS game: Homeworld. It's in outer space, and takes a little bit of getting used to if you haven't played any 3D RTS, but it's one of my all-time favorite games, Strategy or otherwise! :-)

Unusual?
Original war. One of the best strategy games I have ever played, with really clever mechanics, nice story that even branches and ingenious personnel management. Or, better put, a need for personnel management.
Aaaand, as previously stated, Perimeter.

Jsem rád, že jsem to nemusel udělat sám. :)
Yes, definetely Original war. It's different and awsome. Hawg.

"I am happy I am not the only one" in Czech??
If I squint and turn my head a bit to to the left I can almost read that ...

I read it as him saying that playing strategy games was unusual for him, but I could be wrong.

The Guild Gold is classified in the current GOG catalogue as a strategy game....

"Sakra, skoro jsem ani nevěděl, co je to za jazyk, tak jsem tady zangličtinovatěl"
"Well, since I am not the only one <something>, what is this language (jazyk) <something><something> (probably "English" = zangličtinovatě......)
Goddamnit, your written language has too many accent marks!!

Ooh looks like you're right.
I'd say for a first RTS, you should head straight for AoE2 - which isn't on GOG... you learn a bit of everything there.