Brownish water means it's got rusty water... you didn't add coolant, or long time didn't flush and put in new coolant? Coolant has anti-rust properties, plain water doesn't.

I'd try flushing it a few times to get rid of most of the rust build-up and then refill with a cheap coolant + water. If no leaks occurs after a while, I'll continue using it for maybe 20k~40k km, and then drain and put in a good long life coolant like those from Caltex & Toyota. If it leaks, then I'd go get a coolant which seals leaks. Giant sells one such product, but I forgot the brand... maybe someone else can chip in here if they know the brand.

A proper coolant has anti-rust properties.

By the way, I've read that newer cars (with aluminium radiators?) have a warning sticker on the radiator that no coolant is to be added. So, is water alone enough, as aluminium dissipates heat better? Do normal coolants corrode the material?

A proper coolant inhibits rust, raises the boiling point, lubricates the water pump, etc.