The options issue where you have to reset the screen resolution, graphics level, change audio back to stereo, make workers not chop forest, and various other things is caused by the new options that were added for using AI pathing and AI governor stuff.
The place they were added (on the options screen instead of a game option for custom games or on the BUG option screen or just as a value in GlobalDefines.xml) means that they are not stored in the .ini or the save game or in the mod folder anywhere. They are stored in the user's profile, which is in a folder called Profiles next to the cache folder inside the user account's "Local Settings\Application Data\My Games\Beyond the Sword" folder.
The profile with the new options is not compatible with the base game or any mod that does not have the same number of them. Being incompatible (the contents of the file does not match what it is looking for) it reverts to default settings.
In order to play C2C and not have to change the setting every single time, you need to launch it from a shortcut, not launch BtS first and slect Load Mod, since loading BtS first requires the a "normal" profile and C2C reqires a "C2C profile" (with the extra options) and any time you run something that requires one that is not the same as the last one you used it messes it up.
In essence, the problem happens because the number of values in the PlayerOptionTypes enum is different. There are 3 named "PLAYEROPTION_MODDER_1", "-2", and "_3" that BtS itself does not use. If you use only those for a mod then it works seamlessly. If you add any more then you hit the incompatibility issue. C2C now adds "PLAYEROPTION_AI_PATHING" after "PLAYEROPTION_MODDER_3". It's profile file is therefore incompatible with BtS or any mod that doesn't have the same number of options, and vice-versa.
It is possible to work around this via a modified shortcut and a second .ini file. I started messing with this because I need to run mods other than C2C. The Target field in the shortcut used to launch C2C can, instead of the "mod=" qualifier (or, probably, in addition to it), take an "ini=" qualifier. You point that at a new .ini file that specifies "UserProfile = C2C" and "Mod = Mods\Caveman2Cosmos", after creating a second profile with the settings you want to use for C2C.
An actual fix that does not require such a workaround would be to not use so many options that are stored in the user profile. Make the new ones into game options (as per the list you get when launching a custom game), or an option on the C2C tab of the BUG screen, or a setting in one of the GlobalDefines.xml type files.
Step by step method of implementing the workaround
For anybody interested, here is a semi-detailed step by step method of implementing the workaround so you can run C2C and regular BtS or other mods too without having them interfere with each other.
This requires that you use a shortcut to launch C2C once this is set up - do not launch it from the "Load a Mod" menu item from regular BtS.
1) Launch C2C, any way you like this time.
2) Go to the Options item on the Advanced menu and set the options how you want them to be set.
3) Save these as a new profile called C2C via the tab labeled "Other" on the Options screen.
4) Exit the game.
5) Copy the CivilizationIV.ini file from My Documents\My Games\Beyond the Sword (or some similar location, the exact name may vary with windows versions) to the folder wherever you have BtS installed, putting it in the same folder as Civ4BeyondSword.exe. Change the name of the copied file to CivilizationIVC2C.ini (to avoid any confusion in the future, and avoid any possible interference with the regular .ini file). [Edit: fixed this step.]
6) Edit this copy in Notepad, or some similar text editor. You need to change the following 2 settings and then save the file and exit the editor.
6A) change the line that starts UserProfile = to be UserProfile = C2C. (If you chose some other name for the profile up in step 3, use that name instead of C2C.)
6B) change the line that starts Mod = to be Mod = Mods\Caveman2Cosmos
7) Open the Properties screen of the shortcut you are going to be using to launch C2C via right clicking on the shortcut. (Note: Instructions for setting up such a shortcut can be fount elsewhere. There is a such a shortcut in the Caveman2Cosmos folder in the Mods folder for the game that will work if your game is installed in the default location, otherwise you need to point it at the actual Beyond the Sword executable, Civ4BeyondSword.exe, in whatever location you have it installed.)
8) If the Target item on the Shortcut tab specifies mod=\Caveman2Cosmos, delete that part. (It should say this if you have been using it to launch C2C.)
9) At the end of the target line, where it used to say mod=\Caveman2Cosmos, add this: ini=CivilizationIVC2C.ini. There should be a space before the ini=.
With these changes, this shortcut should now launch C2C and make it use the new profile instead of the default profile.
You will probably need to reset the options for regular BtS (or some other mod) once, to get the settings for the default profile back to what you want them to be.
After that, they should stay set to these settings since C2C now uses a different profile and will not mess with the default profile as long as you only ever run it by using the shortcut.