Right then: if you have no 'Conquests' directory (and hence no Civ3Conquests.exe) then you almost certainly have Vanilla, v1.07.
(Yes, that's quite possible. I also bought Civ3 on CD in 2009, through Amazon, so I didn't know exactly what I was getting until it arrived in the mail -- turned out to be the Atari-published Vanilla 1.07 version, from before Civ3 rights got sold to 2K Games)
Compared to Conquests(/Complete), original Civ3 includes:
- 16 civilisations (vs. 31)
- fewer government types (no Feudalism, no Fascism)
- fewer standard-issue units (e.g. no Medieval Infantry, no Guerillas, no Cruisers, no TOW Infantry)
- an unmodified Industrial-Age tech-tree (Steam-power still gives Ironclad ship-units, Radio is a required tech)
- fewer Wonders (no Mausoleum, no Statue of Zeus, no Temple of Artemis, no Internet)
- no additional 'Conquests' scenarios
And v1.07 also has a few bugs (mainly in the Editor, but still...). So yes, you should patch it, and you'll need only the
'Vanilla' 1.29f patch. I used this file from CFC without any problems. Basically what it will do is replace the current version of your .exe file with an updated version. So just to be safe, before installing the patch, you should backup your current .exe file somewhere else (and/or copy/ rename it as e.g. 'Civilization3 v107.exe'). That way, if you find that the game doesn't work after patching, you can simply delete the newly installed .exe and rename the original back to 'Civilization3.exe' (if you want to go back to using it).
Even if the patch is successful, some users have reported not being able to continue with games started under a previous patch version -- but if you can, expect some game behaviours to change a little (e.g. 5-hitpoint 'elite' units which have aleady produced a 'Great Leader' now get tagged with a '*', and can be renamed -- which is really useful for deciding which elite unit to attack with next when 'leader-fishing').