I'd recommend using the WS2811 strip with the IC built into the LED. Fewer pins, therefore more robust. I use the gel coat variety for a bit of added strength and weatherproofing.
Unless you fancy yourself as a coder or you know someone who is good with Arduino (or similar) – and is up to the job of doing the math to produce a water pattern, I recommend you go for an ‘off the shelf’ controller. On a budget, your best bet is to get an SD Programmable controller from one of the online Chinese suppliers. You should be able to get one pretty cheap. Look for one that comes with software that will allow you to import video files. With a bit of experimentation you should be able to create/plagiarize a video or animation of the effect you want and convert it into a data file for the controller to play back on your LED panel.
Be wary of adding too many LEDs to each controller port. The WS2811 isn't that fast, so the controller may not be able to update all the LEDs quick enough if you push it too hard.
Also, you'll need a lot of power. To use BBadger's example, 108m of 60 LED/m strip could peak as high as 160 Amps at 12V. Normal running of a pattern would probably be around 60A at 12V. Thus, you need to inject power at regular intervals. Of course, if you were using 5V strip, you’d need some very heavy duty wiring indeed
…Obviously, don’t use my figures – check the precise spec of the strip you order, and then test a short length with a multi-meter as the specs are sometimes wrong
If you’re using 5V strip, you'll be needing a bunch of very chunky regulators...
Given your budget, you'’ll probably have to stick to about 30 LED/metre. Obviously it won’t give you as much detail, but (for example) the coat in my avatar pic is 32/m and as you can see, the effect is still good. This would allow you to use a cheaper controller, have easier to manage power requirements and be half the price. If ordering from China, always get more than you need - a spare or two may well come in handy!