参照 means actually reading the reference, while 参考 generally refers to using existing knowledge/idea. I.e. 参照 is narrower than 参考; everything that can be 参照ed can be of 参考, but not everything that can be of 参考 can be 参照ed. E.g. your experience leading a project would be of 参考 when leading another project, but you won't be able to 参照 it because it's not something you can literary read. Conversely, if someone is operating a nuclear power plant you want that person to 参照 the user manual rather than taking the user manual into 参考; 参照 would imply he'll follow it to the letter, whereas 参考 leaves some room for improvisation.
参照する seems more common than 参考する
参考する is not natural.
参考にする seems more common than 参照にする
参照にする is not natural.
参考になる more common than 参照になる
参照になる is not natural.
the keigo form ご参照ください seems more common then ご参考ください
It would be ご参考にしてください, but this can only be used by someone of higher rank than the audience as it sounds condescending. Asking somebody to literary look up the reference is OK (e.g. please see page 30 in the usage manual), whereas asking someone to take something into consideration can sound more impolite (e.g. please take our best practice into consideration).
By extension, when talking about my own intentions to consider something (e.g. something like 「○○を参照するつもりです」 or 「○○を参考にするつもりです」), which of these is preferred?
If you mean you are literary going to look something up, use 参照 whereas if you are referring to your general intention to consider something, use 参考.