First off, kudos for recognizing that sound is important!
I don’t think a couple hundred dollars will cover it, because there are a few basic pieces and parts that add up, even on the low-budget end. Fortunately, there are a few lower-cost options that can get you started.
Before I list that stuff, though, I highly recommend that someone on your team step up to take on sound and learn how to get it right. Having one person specialize in any given area makes the whole team stronger, as opposed to trying to make everyone interchangeable multitaskers. If everyone‘s attention is diluted, everything suffers. I mentioned this in your other thread asking about good starter cameras.
While professional sound these days is recorded with some very complex, and very expensive, systems, sound for film and TV was once accomplished simply with a boomed mic and a recorder. So that’s where we’ll start. You need a good mic, an extendable boom pole to get it into the action, proper suspension mounting and windscreening, and cable. Then, you need a good recorder or mixer-recorder, and trustworthy headphones. Last, you need a way to sync the sound to the picture in post.
On the most basic level, I’d recommend the Tascam DR-60D mkII as a decent and reliable recorder. $199
You’ll need a couple of SD cards (never have just one), about $25.
There‘s also a good, low-cost bag that comes with (rudimentary but functional) harness, from STRUT. $119.99
For the mic, the Audio Technica AT875R is a really good bang-for the buck option. $149
For wind protection, the Rycote Classic Softie. $99
And you’ll need a shock mount to avoid handling noise from the boom. Rycote InVision INV-HG mkIII. $69
A 9’ boom pole is more than enough to get you started. The K-Tek Airo is actually 10’, but isn’t internally cabled. $114.95
So you’ll need a 15’ XLR cable, about $25
For headphones, the Sony MDR-7506 are pretty standard. They’re also accurate. $84
Last, you’ll need a dumb slate (clapper) to slate each shot for sync in post. There are a couple good options from Elvid. $34
The DR-60D mkII doesn’t allow much room for expansion when (not if) you hit the point where you need to add wireless, so alternatively you might look at the slightly larger DR-70D ($279) and Strut case/harness ($134). This is all about channel count. A boom and 2-3 wireless can cover a lot of ground.
I know, it’s a lot more than you were wanting. Anything cheaper is, well, cheaper.
Just curious: which cameras did you end up getting, and what types of projects are you wanting to focus on?