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I'm about to post an ad for our company survey but I'm not sure which of the following (the position of should) is correct.
Take the survey on which computer should our company get next.
or
Take the survey on which computer our company should get next.
Syntactically (and semantically), OP's sentences are equivalent to...
1: Vote on which computer should we get
2: Vote on which computer we should get
...which we can easily convert to something common enough to search for on Google Books...
3: Tell me what should I do (11,200 results)
4: Tell me what I should do (99,700 results)
So if you believe there's safety in numbers, go for the second version.
Look at some of the results for #3 above and you'll see they often have any or all of these features...
1 - a comma or colon after Tell me
2 - the words after Tell me enclosed in quotes
3 - the word Which capitalised
4 - a question mark at the end
That's because the text after Tell me (after Take the survey on in OP's example) is a question.
Note that both forms are perfectly valid, and unproblematic in speech. But in writing OP will have to address punctuation. As there's no single "correct" written form, whatever choice he makes will seem "wrong" to some people. So that's another reason to avoid the first version.
