You dont need to dump a barrel of cash on equipment. There are some extremely decent rod and reels out there that could stay under $300 for the set. Cabelas has some fine combos. Heres one that would do fine for a beginner. Cabela's Prestige® Fly-Fishing Outfits : Cabela's
Make no mistake, this is very decent gear that will get you deep into flyfishing. If its something that snags your heart, youll be like us and eventually have a whole quiver of rods/reels. At which point this one would still serve its purpose.
I assume you are thinking freshwater? My suggestion woud be to get a 9' 5wt. 4 peice rod. Put a matching 5wt. weight forward, floating line on it. (dont skimp on the line, RIO Selective Trout is a good one) Now, get a handful of nymphs, small wooly buggers and dry flies and go to a panfish pond. Play with those fish until you start catching them. Get some confidence. Nothing beats experience and experimentation. Be very careful of reading too much. "Analasys Paralisys" is rampant in flyfishing, especially for beginners.
After you've put in the time at a local pond/lake, you'll know when its time to take the next step. Only you will know what that is. And youll definitely know what to spend the rest of your money on.
Hope this helps and welcome to the wacky world of information overload