Alright, which Ill try that, but still there must be some must haves or at least important ones, which should I try to avoid/must build?
Note that the wonders explained in the top menu of this site is of Civ3 vanilla - not civ3 complete (C3C). The great wall was changed and some others.
As always: it depends.
Look at what a Wonder does first before you build it.
I try to avoid all wonders that go obsolete. Maybe one or 2 like Lighthouse. That is just because faster ships saves so much time. I feel I lose many turns just shipping units. Actually, I mostly make Magellan's - you don't sail that far in the age you have the Lighthouse. It's the same wonder - only later in the game.
Are you really going to need a Great Wall against barbarians or in-town fighting? Ok, it's easier now to keep captured cities. Hm. Ok. You'd better fight on the borders, on hills and mountains... and building a wonder for the barbs is just wrong. WRONG I TELL YOU!
I used to like Statue of Zeus or Knights Templar, because it creates an Ancient Cavalry or Crusader respectively every 5 turns. I don't build it much lately. It's quite a lot of shields for x-amount of units.
I love Leo's (pay half for unit upgrades). Saves A LOT of money. Money that can be spent on science, happiness and nukes.
Pyramids sound nice, but it's effectively building all granaries for all cities in one city (often one of your early cities). I wouldn't do it, since you can hurry a granary by cutting a nearby forest with the workers that that early city is producing. But the Pyramids is 400 shields and a granary 60. So 6.666 or more cities and you have made a profit. But it's many turns that one of your main city can't build anything else.
Theory of Evolution (2 free techs) - that one is one I love to rush if the opportunity raises. That wonder often is the turning point in many games. After those techs, I never look back - since it is close to rails. Rails + ToE = Whooooosh!
If you can combine Copernicus and SETI... nice combo. Then you double your double science output for that city. You double your science in that city twice. Stacking the effect is worth it. I must admit that I hardly ever do it.
Love Smith's - pays the upkeep of markets, banks, harbors and airfields.
Same for Universal Suffrage. Reducing WW is good...
I don't build the United Nations wonder, that's because I like the Manhattan Project.

Cure for cancer - how can you be against it.
On a side note; there are many kinds of cancer. Cancer is the word used for about 200 different diseases - so there's not going to be one cure or one treatment. Development for all 200 is taking place as we speak. We are getting close to developing better and humaner methods. But if someone makes a breakthrough development today, it will take about 7 years of proper development and clinical trials before the treatment is on the market. Not because the pharmaceutical companies don't want it released, but because every medicine and treatment must be tested and safe to be released on sick people. That's international law.
On with civ3.
As for the Small Wonders - I try to build them all. They are a nice bonus.
Make the Military Academy in your more/most productive city. Maybe you're lucky and find a city that can make the Iron Works.
I don't build the SDI defense though. If I'm nuked successful or not, I'll live and I'll retaliate. They will be throwing rocks after that.