RE: Fly Rod
It's tough to be specific on price and brands as "not too expensive" is a very relative statement. One thing that's important to note is that your rod weight is directly related to your reel weight. You are going to have problems casting if you stick a 2 weight reel on a 6 weight rod, so I'm not sure if this is going to effect what you need to buy or not.
That said, my recommendation would be to go to a good quality fly shop (something that stocks more than just Orvis stuff) and tell them you are shopping for a new rod. Rods come in different length, line weight, material (I think it's safe to assume Bamboo is out for you), action.
By going to a store, you will accomplish a few things:
1. You will see good quality equipment that may or may not meet your budget.
2. You will be able to test different rods and get a feeling for the action you like (most people starting out like a medium flex rod, but don't automatically conclude this... go find out for yourself).
3. Biggie... the salesman, who probably is a fishing guide or knows how to fish, will help you learn the basics of casting or help you go beyond that if it's where you are right now.
After that, you will know what you like. You can choose to buy a rod or rod/reel/line combo from him or go to your local walmart and pick one up, but at least you will know what you're looking for.
Every rod manufacturer has a combo package where you will drop between $ 100 - $ 300 for the whole kit.
As far as the weight of the rod, I wouldn't worry too much whether it's a 5 or 6 weight, but don't buy anything other than a 5 or 6 weight. These sizes will pretty much go anywhere. I have a 5 weight which I fish for smallmouths on the lake I live on and bring it to New Foundland where I catch Atlantic Salmon. A 6 weight would do the same thing, but what's more important is the level of confidence you feel with whichever rod.
Man, all this talk about fishing is making me realize that our newfound winter really blows up here.
Cheers,