If I have the money and find one early, usually military so that I can focus production on other things. Generally I find the strategic importance of allying close CSes (or, if I have an early war, CSes close to my enemies) and those with luxuries I need (what do my cities demand for We Love the King?) can outweigh the benefits of CS type - you can quite often get early influence from assisting them against barbarians (not so good with more distant CSes, especially since if a distant CS wants an encampment wiped out, it will probably be done by someone else before you get there), and they can act as a military bulwark against neighbours. Occasionally the diplo hit from 'competing for the favour of the same CS' is something I'm not willing to risk depending on my neighbours and diplo situation more generally.
In other words, my relations with CSes are very map-dependent, perhaps most of all in the early game, but given the choice and equivalently valuable resources I'd prioritise military CS, which unlike the others are only really useful in the early game. You can usually recoup the financial investment from early alliance with military CS with two or three units gifted from them, and they remain yours once the alliance is over - culture and maritime really require maintenance to keep the bonuses flowing, since the per turn benefits are small, and I'd rather invest in those in later eras when the CS bonuses are larger.