I absolutely love this. People say Bethesda's writing is terrible, yet there's clearly no "right" answer here.
The idea of a Minutemen/Railroad alliance is very tempting. On the surface it seems like the most moral way to go, albeit with a nice dose of logical fallacy with how the Railroad want to go about things. It would put the Commonwealth in a weaker state than the other options, but the potential to grow into an NCR like faction is there.
A Minutemen/Institute alliance could go really far too, although it's questionable whether you could reform the Institute enough to make a difference. You only have to look at the Brotherhood of Steel to see that one leader with moral aspirations can change the organisation short-term, but not necessarily invoke long-term changes. At least with a Minutemen/Railroad alliance you're invoking the right set of values from the conception stage; not trying to reform something that's been going for ages.
I can't imagine the Brotherhood of Steel would accept a long-term alliance with the Minutemen. At some point they'd simply annex the organisation and take over completely. They don't like sharing power. That said, if you don't mind the purging of Mutants/Ghouls/Synths then they're a pretty smart move tactically.