Confession: sites I maintain have different rules for Cache Control mostly based on the default configuration of the server followed up with recommendations from the Page Speed & Y-Slow Firefox plug-ins and the Network Resources view in Google's Speed Tracer. Cache-Control is set to private/public depending on what they say to do, ETag's/Last-Modified headers are only tinkered with if Y-Slow suggests there is something wrong and Vary-Accept-Encoding seems necessary when manually gziping files for Amazon CloudFront.
When reading through the material on the different options and what they do there seems to be conflicting information, rules for broken proxies and cargo cult configurations. Any of the official information provided by the analysis tools mentioned above is quite inaccessible as it deals with each topic individually instead of as a unified strategy (so there is no cross-referencing of techniques).
For example, it seems to make no sense that the speed analysis tools rate a site with ETag's the same as a site without them if they are meant to help with caching.
What are the hard and fast rules for a platform agnostic Cache Control strategy?
For the record though here are the hard and fast rules:
If the file is Compressed using GZIP, etc - use "cache-control: private" as a proxy may return the compressed version to a client that does not support it (the browser cache will hold files marked this way though). Also remember to include a "Vary: Accept-Encoding" to say that it is compressible.
Use Last-Modified in conjunction with ETag - belt and braces usage provides both validators, whilst ETag is based on file contents instead of modification time alone, using both covers all bases. NOTE: AOL's PageTest has a carte blanche approach against ETags for some reason. If you are using Apache on more than one server to host the same content then remove the implicitly declared inode from ETags by excluding it from the FileETag directive (i.e. "FileETag MTime Size") unless you are genuinely using the same live filesystem.
Use "cache-control: public" wherever you can - this means that proxy servers (and the browser cache) will return your content even if the rest of the page needs HTTP authentication, etc.