I'm looking to have that very greenish cast appeal of the Matrix. I want to get a cheap way of doing this, possibly a color/light filter, rather than doing major lighting/color editing during post. =)

The answer to similar questions and more specific to the Matrix
one has been answered quite a few times already, please browse
and search the forum. That's why all the posts are here.

1) why would you want a filter? This leaves you unable to change
the effect in post if it turns out too green for example. Filters can
be very handy. But usually filters that mess with the picture are
best left to post for more control (exceptions being UV filters,
ND filters, grad filters etc. etc.). Yes, some people prefer filters,
but not a whole lot.

2) if you just want the green color cast you can easily shift the
color to green with any NLE's color adjustment tools (there really
is no simpler way)

3) don't just try to copy. Find your movies own visual style

Back to the topic of searching. I clicked on the search (in the upper
right corner), selected this forum from the list (Towards a Film
Look Using DV), entered 'matrix' as the search criteria and hit
search. On the first page I found the following hit:

Matrix Look (http://www.dvinfo.net/conf/showthread.php?s=&threadid=17640)
(it specifically even talks about the look you want through a filter)

As well as several other threads that talk about getting certain
looks (again referencing The Matrix on some threads).

Yes, I agree. How about experimenting with the Chroma settings, White Balance etc to achieve it in camera? I did a simple WB and was surprised at how matrix like it looked. And I dont just mean green. The flesh tones were still somewhat intact.