As the other answers have mentioned:

- "Sarah and us are going to build..." or "Us and Sarah are going to build..." is *proscribed* by the authors of mainstream grammar guides. Linguists generally disagree with the idea that an objective-case pronoun in ungrammatical in this context (for an explanation of some of the relevant literature, see my answer to *[When do I use “I” instead of “me?”](http://english.stackexchange.com/a/358552/77227)*); in fact, using a *subjective* pronoun in these contexts seems to be what's unnatural according to the internalized grammar of native speakers (which is why they need to memorize rules to be able to use subject pronouns "correctly"). But that isn't likely to change the mind of anyone who views it as "incorrect", and in this particular case, the objective pronoun sounds awkward to most people anyway.

- "Sarah and we are going to build..." (or "We and Sarah are going to build...") is what you get if you mechanically apply the "remove other words and check which pronoun you'd use" rule. However, a linguist would say that rule doesn't necessarily produce grammatical sentences, since as mentioned before, the use of subject pronouns in coordinate noun phrases like this is arguably not "grammatical" at the deepest level in English. And any prescriptivist who doesn't have a tin ear would agree that this phrasing is, at minimum, infelicitous.

The natural construction here in my opinion is to use "with" instead of "and", as thesaundi's [answer][1] says and as [Eldroß][2] suggested in a [comment][3]:

- "We are going to build an aircraft with Sarah."
- "Sarah is going to build an aircraft with us."

Nobody would interpret the first as meaning Sarah is the material with which you're building the aircraft. It's a completely harmless ambiguity (of a type that is ubiquitous in English), and it is completely disambiguated by prior knowledge ("Sarah" is a person's name, and we don't build aircraft out of people) so it's silly to avoid this structure just because it is technically ambiguous. You might as well avoid "are going" because it's ambiguous between referring to plans for the future and referring to literal motion.

Or you could say something like

- "Sarah and the rest of us are going to build an aircraft."


  [1]: http://english.stackexchange.com/a/6022/77227
  [2]: http://english.stackexchange.com/users/2172/eldro%C3%9F
  [3]: http://english.stackexchange.com/questions/5995/bob-and-us-or-bob-and-we-or-bob-and-ourselves/364018?noredirect=1#comment9065_5995