As a rule of thumb, which Magento 1 caches should be cleared after installing an extension?
Sometimes, especially for large websites, flushing the cache from the Admin can be a major process (its much easier to clear the entire cache with ssh). Especially websites with tons of pages, rebuilding the full page caches can take quite a bit of time.
The absolute minimum caches required to flush really depend on the extension.
Used to store extension info including everything in the etc directory. Configuration cache is also required to be cleared in order to run installation scripts. ALWAYS Required.
Used to define which blocks (and templates) are loaded for any given page. Required only if new extension includes a layout file.
Blocks HTML output:
Cached blocks that are pre-rendered and reused for multiple sessions and users. Required only if new extension configures 1+ blocks to use the cache.
Full Page Cache:
Similar to the Blocks HTML output above, this feature pre-renders entire pages. (Enterprise, Extension, V2) Required if new extension includes any frontend elements.
Caches the results of translation functions (
echo $this->__('Something');) Required if website uses translations
Not really sure... assume a database optimization.
EAV types and attributes:
Caches the EAV models and attributes including any custom product attributes. Required if extension adds/modifies any EAV model
Web Services Configuration:
Caches the API XML files including WSDL. Required if extension includes API additions