Include VOIP!

Could also run Mumble on the server and control it internally via it's built-in Ice remote system, and Mumble also supports positional audio. Open source, mostly BSD licensed, although a couple of parts may need licensing if it's physically built-in to the client as opposed to remotely controlled. Audio quality is excellent though.

VoIP must be easy or in general it isn't going to get used.

It's cool that TeamSpeak has an API, but I feel like people still aren't going to tend to install it. If this is made as easy as possible, and the game told your to install TeamSpeak during installation and at other times, it could encourage people to get it going.

Ideally I'd like it to also support Steam, but if it's only going to work for Steam-based versions of the game, that kind of sucks. Everyone doing Kickstarter isn't going through Steam.

Does anyone know for sure if you can or cannot use Steam features in a non-Steam game? Will I still be able to press Shift+Tab to bring up the Steam chat interface while I'm playing the game?

I'd be one for VOIP to be invite-based, like "Your team-mate wants to chat, accept/decline". That would be a handy feature for higher-level matchmaking team games, as franticially typing orders can be a tad unweildy in the middle of a click-fest

I'd definitely like to have voice chat in-game. A lot of times I'm in a battle in FA and I need to yell to my opponent, "No, do this, move there!" but I don't have time to bring up the chat box.

VOIP is on as default on most Source engine based games and it's fine. You just click on peoples names to mute if they're playing stupid music or whatever. Or turn it off altogether so you can't hear everybody. It would be easier in an RTS than a FPS because you've far less players in a match.

Of course it's not good all the time but when it does work it makes things so much more social.

I'm not a great fan of reinventing the wheel, in particular when everyone has an own idea about the features of that wheel.

Every online player I've met has his own preferences concerning VOIP, from not at all, over specific programs to existing servers they want to use.
Therefore, I would prefer reserving VOIP to external applications.

The part of inter team communication I would focus on is the possibility of effectively sending team mates visual hints and clues. (target markers, regions, routes etc)

Only include built in VOIP if it is good and works reliably. If it's not as good as the others it's not worth including in your game.

Given the budget, I wouldn't blame them in the least for just not bothering with voice support since there are free third party options available to handle that.