If you ask any fly fishing angler out there what is the best first rod and reel setup you need, you will get a different answer from everyone. Picking your second, third, or even seventh rod you will have some very specific purposes in mind and still get a lot of different answers. Your first fly rod and reel should be a good general-purpose setup that will be easy to use in almost any trout stream in the region.
For the love of Zeus, you don't want to look like the dopey guy in the Symbicort commercial that has a crappy M*A*S*H hat, is fishing for brook trout in a creek with a large arbor saltwater 9 wt reel and 15-foot fly rod setup with a real bobber on your line. I'm not saying go spend all your 401k money, quite the opposite. Don't spend a lot, but get something that makes sense to get started within our region to fly fish for trout.
If you are just getting started, you will likely want a 5 weight (wt) 8'6" - 9' graphite, medium-fast action fly rod. This is an all-around great fly rod for beginners. I like the four-piece rods as they travel better. Make sure whatever setup you get has a good rod tube to keep it protected when it is stored away or while in your vehicle. You can expect to pay about $100 or more to get started.
To select a fly reel you match the weight of the fly rod to the corresponding reel. If you get a 5 wt rod then you get a 5 wt reel. Nothing fancy needed when you first get going, it's really just a spool to reel in your fly line. A line holder if you will. No need to drop a car payment just yet. Starting at around $100 will get you a good quality machined aluminum reel. While as little as $35-$70 will get you into the game with a stamped steel or synthetic line holder.
Be sure to complete your setup with a weight-forward fly line that matches the weight of your fly rod and fly reel. Remember, unlike a spinning rod and reel, the fly line is what carries your fly. So stick with the 5 wt again for your fly line and that will run you $29 - $59.
Tapered Leader and tippet
A knotless tapered leader is usually a 9' section of special monoline that connects the end of your fly line to some ~30" of tippet and then your fly. With proper casting, the tapered leader and connected tippet provide a natural presentation of the fly onto the water. The different x's and lbs test of the leader and tippet should be changed during the season and conditions where you fish.
A 5x trout leader is a middle-of-the-road and good starting point in the early season. You will likely be fishing more streamers and nymphs in March and early April. When dry fly fishing on top or for smaller trout you can get to smaller 6x leader and tippet setups. You will want the presentation of the fly to be a little more delicate and the right tippet can make a huge difference. You should pick up a few leaders that will run you about $3 each and a spool of 30' 5x - 5lb test tippet is about $5. Think five's for now.
I want you to explore more of the details on these setups and ask others. Just remember when you share with someone the setup I am suggesting 99 of 100 people will say it is wrong and I am an idiot. Hopefully, in 30 years you can be an idiot just like me. Check-in on the forums to do some research. Get started and then modify your setup as you see fit and what works best for you. I never use knotted leaders for example only crazy people use that crap. Kidding of course...a little.
The dollar amounts I discuss are good starting points and you will do just fine. You can spend more if your budget permits or you just got a good tax return. Maybe your wife just snuck in some new clothes from Anne Taylor with the dry cleaning and it's your turn. Been married 25 years and know a lot of these tricks. Just say there was a great 50% off sale. I hear that one all the time.
So where do you buy this gear? Please look at the sponsors (Allen Fly Fishing) on the site that offers the gear discussed. There are plenty of great brands and choices. But, mainly because I trust them, they have a good range of products and warranties they stand behind. They are available to answer questions for you through email, on the phone or in the Shop Talk Forum. You will find many other members on the site providing feedback about their gear in Gear Talk or the Beginners Forum. If you want some more traditional conversation go to a nearby fly shop and get some answers there too.