I don't know if I was just lucky or what, but I have Civ3 running fine on Win XP home with the second patch and everything looks pretty!
Here's my recommended step by step guide.
1) If you currently have the patch installed, use add/remove programs (from Control Panel) and remove
the patch.
2) Take a copy of your SAVES folder in Civ3 (I dumped it onto my desktop) - assuming you have saved games you want to continue.
3) Uninstall Civ3.
4) Reinstall Civ3 - don't use any modpacks or amendments - just plain vanilla Civ3.
5) Copy contents of your previous SAVES folder into the newly installed SAVES folder.
6) Apply latest version of Civ3 patch. If you're not sure you've got the latest - download it again! (I mentioned sizes of the two patchs in a previous thread but I was a little imprecise. If you check the properties of the civ3v116f.exe, the size should be 7,663,795 bytes - the first version was 7,663,745 bytes).
7) If you're running Win XP - try turning on CLEARTYPE (available via the CONTROL PANEL - display/appearance/effects - choose CLEARTYPE in the pulldown box after ticking the 'Use the following method to smooth edges of screen fonts' box). This step should get rid of the shadowy text (or at least reduce it).
8) If you normally run your system in a resolution higher than 800x600 (for instance, I use 1152x768) - edit your Civilization3.ini file and add a line saying KEEPRES=1.
9) Cross your fingers and try the game.
That was what I did - everything seems fine.
I'm not running the programs using compatibility mode - didn't seem to need it.
Note: DO NOT ATTEMPT TO RELOAD A SAVED GAME IF YOU SAVED IT WHILE THE FIRST PATCH WAS INSTALLED. You'll have to revert to a previous version (you kept them didn't you?) or maybe a previous AUTOSAVE version.
Finally, if are running an nVidia video card on XP and you still have the slow scroll problem that people previosly had (which is not related to the patch) checkout the thread somewhere on this forum which offers a link for some beta drivers - they solved the scroll problem for me. Alteratively you can revert to older version of the drivers (but I don't know version numbers etc.)
Keep the faith people - I think we may just be able to get through this crisis.