First of all i would go with Nikon\Canon, they have the most options and there the most reliable to invest money in, if its body or lenses.
with 600$ you can get as your friend says a 'older' body like the Nikon D3100, or the Canon T3i with a 18-55 kit lenses (the Nikon 18-55 kit lens is known to be slightly better then the Canon 18-55 kit lens), depends on what feels better handling, try it in the shop, hold it in your hand, take a few pictures, take your time, don't get bullied by the salesmen.
If you can push the price lets say to 700$ you can get the new entry level DSLR from Nikon, the D3200 (it has a guide mode within the camera which is good for beginners), Canon didn't come out yet with a new entry level, but they will soon.
with 600$ you won't get a lense for EVERYTHING but the 18-55 will get you MOST of what you want to shoot at first, the telephoto lenses for wildlife and sports are relativly expensive and out of your budget...use the 18-55 until you can save for a better lense, say like to shoot in low light at night and stuff like that, you will probably need a prime lens which i usually recommend for folks after they use there kit lens for a while and want to upgrade, if there isn't enough zoom range, use your legs

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For example when i bought my first DSLR 1 year ago (the Nikon D5100), i bought only a 35mm 1.8G prime. of course its not for everybody and most pepole that are starting out are more comfy with the 18-55, but folks said that its much better and i should use my feet to get closer or longer, it also makes you slimmer and it also gives a special feel to the pictures, and you find yourself "working the scene" much better, because you have to move yourself to get the shot and not just zoom with your camera. plus with a prime you get all the benefits of low light and natural light photography, which you CAN do with the kit lens but not as well as the prime (slower and you'll have to use high ISO) - anyhow i don't want to confuse you with a lot of information, so i'll leave it at that for the time being.