Well, I was considering buying some Ithilien rangers, because cheap bow troops with a spear to support my WoMT sounded pretty beast. But I was wondering, could you have Elves with bows and spears? There doesn't seem to be anything saying that they can't, which seems a bit overpowered, all things considered.

Nothing prevents you from buying both a spear and a bow. In fact, it is a very common tactic to combine your archers and spearmen. But remember, if you play Minas Tirith and add Elven archers, you must have other Elves as well as the bow limit is applied to each allied contingent, not the whole force (just a reminder).

Thanks. I like allying Elves with Minas Tirith, and I wanted a warband that could both shoot and fight, so I didn't have to support it with one of my other units when things got hairy.

Every bowman can shoot and fight, they all have hand weapons. Giving them a spear only lets them support, but you don't need it to throw them into the fray.