For what you're wanting to do, you could probably get by with the cheapo microphone that comes supplied with the computer sound card. But it might be worth it to you to get a better microphone. The little Panasonic capsule mics don't cost much at all, and they'll work very well. You can trust the data you gather with them. You may need a microphone preamp to use them, however. Depends on the sound card, some will work without the preamp.

You'll probably want something to hold the microphone capsule. You can make a great little boom for it using a piece of plastic tube that's normally used as the supply line for toilets. They're available at any hardware store and the mic capsule press fits nicely in the end. The wire can be run through the tube and that makes a nice clean boom mic.

This may be a little more ambitious than what you wanted just to find the polarity of your tweeters. But once you're setup and running, you can do a lot more with it. It's a fully functional acoustic measurement system that you can use to help build new speakers, design crossovers or setup your sound system in your home.