we're putting gutters up because we want to do rainwater collection. all you need are the gutters and a collection tank (some sort of water-tight barrel or box).
we're using a 55 gal metal drum (the kind oil is transported in, but these are food grade) that we picked up for $17. you just need one usually. all you need to do is put your gutters up so that they have a slight slope toward the corner/side where your collection tank will be and cut a hole in the lid of your collection tank. the downspout would usually go all the way to the ground and deposit the water in a drain, or just in a puddle in your yard. instead, the downspout now goes straight into your collection tank and gives you all kinds of free water!
if you want, you can put a spigot at the bottom so you can easily fill your waterers. you can buy a spigot at most hardware stores and then you just need to drill your hole about 5 inches from the bottom of the barrel. this will gravity feed the water so you don't need a pump! (you probably want to elevate the collection tank so it's easier to get your buckets under the spigot.)
you do need to filter out leaves and whatnot somehow, and keep it algae and bug free. if you use a plastic collection tank, you can just cut a hole in the lid directly under the downspout and put in a hardware cloth screen. if you also use plastic waterers, you can treat the water in the tank with apple cider vinegar to discourage bugs and algae (never use ACV with metal!).
if you use a metal collection tank, the downspout needs to go into the tank with the lid fairly tight around it. use the hardware cloth to make a basket that hangs inside that you can easily clean. keeping it sealed like this should also keep the bugs and algae out.