You're sure to get a number of suggestions on this question but you can start out fishing with something as simple as a spincast rod and reel and a few small lures/spinnerbaits or plastic worms. I guess it depends quite a bit on what part of the country you are in. Out west where they have a lot of trout streams I would imagine a fly rod would be the equipment of choice. Up north in your country a heavy bait casting road and reel or salt water type spinning rod would be more appropriate. When I visit my friend in Batchawanna Bay and we fish the coves of Lake Superior we use fairly heavy equipment. Those Lake Trout and big Northerns can wreck a small setup.
Around here in Indiana I use a medium spinning reel for bass and catfish and an ultrlite spinning rig for panfish. A big bluegill on an ultralite can give quite a fight.
You can start out pretty reasonable. Its when you get hooked that it can get expensive. ;D One can start out as simple as buying a kids rod and reel for under 20 bucks and get a few lures for a couple bucks.
Now when you get hooked next comes the fine fly rod, or a boat and heavier equipment etc. Stop by Sam's Camp sometime and we will see about getting you started.
Good question Steve, and one I was going to ask myself. I started as a kid when my father made my first fishing rod from a bamboo cane and made my first reel from an empty cotton spool and a few bits and pieces of hardware. This was as low budget as it gets. At the time, I fished for trout in our small local river.
My daughter came home from Brownie/Girl Scout Day Camp many years ago with a 21" Northern she caught with a bamboo poll and a piece of summer sausage from shore . It didn't entice her to take up fishing and she never knew until years later that we never ate that fish because the leaders didn't pack it in ice for the hour ride home. The fish we ate was one we had caught on Lake Michigan. So the moral of the story is you don't really need lots of expensive equipment .
I agree with Ned about the pocket fisherman. My dad had one and it was junk. There are some nice collapsible rods on the market tho that will take an ordinary reel. I carried one in the trunk of my company car for years and used it whenever I got a chance to go fishing while on the road.
A spinning rod and reel with a line test rating of around 5-10# should take care of most freshwater fishing, bar salmon, steelhead, big cats and other such piscine monsters. A supply of hooks and sinkers and some live bait or in the case of trout and cats, cheese baits or stink baits respectively. I kinda like the Mepps spinners for trout in lakes.
Now if you wish to go crazy, there is always fly fishing or bassin'. With both sports you can wind up with a rod and lure collect that is barely luggable in the field.