Basic Gear for the Beginner...
Fly rod, reel and line:
When it is time to purchase a fly rod and other necessary gear, there are some very important things to know and it can be very confusing for a beginner. The most important and necessary equipment is a properly setup rod, reel and fly line. I mention all three of these things together because all three need to work together...in fact, they need to be "matched". When I say "match", I do not mean color coordinated. I mean that the weight (wt) of the rod (typically 2 wt. to 14 wt.) must closely match that of the fly line (also typically 2 wt. to 14 wt.). The reel too has a weight (wt) associated with it (typically 4-5 or 7-8).
Just know for now that "matching" the "weight" (wt.) of the rod, fly line and reel are very important...not just for the beginner, for all fly fishers. Like fly lines, weight is also closely associated with fly rods. All fly rods are designed and manufactured to cast a specific weight fly line ...so a 5 wt. fly rod is designed to be used with a 5 wt. fly line. This can vary by a line size in some instances but it is a very good rule of thumb. Matching the weight of the rod and fly line is most crucial. As you will learn when starting to cast, if the weight of the rod does not closely match that of the fly line, it becomes more difficult to get the fly rod to "load". You can think of "loading" as making the fly rod bend during the casting stroke. All fly rods are designed to properly load when the rod weight closely matches that of the fly line. If they do not closely match, fly casting is much more difficult. In fly casting, you always want the rod to do as much of the "work" as possible. When a fly rod "loads" (bends), it stores energy that is released as the rod straightens and this energy is your friend.
As I mentioned above, fly rods and lines are rated from 2 w.t to 14 wt. The smaller weights are for smaller streams and smaller fish and the larger weights are for bigger water and fish. A 12 weight is a typical rod for fish like tarpon and other fish that weigh upwards of 50 pounds.
In will just briefly mention fly lines. In recent years, fly line manufacturers have made a generally confusing mess of what used to be pretty simple. Without getting into all of the specifics, Fly lines can generally be divided into three types...floating, sinking and intermediate. Floating lines float, sinking lines sink and intermediate lines (not too common) have a "neutral" buoyancy. Fly lines are typically 90 - 105 feet in length and come in many colors. In recent years, all of the manufacturers have created fly lines with different tapers and they call them things like "Bass Taper"...supposedly this has a taper that is helpful when casting large wind resistant bass poppers, etc. There are now many "specialty" lines that have created the "confusing mess" I referred to above. For a beginner, I would suggest a floating line with a weight forward (WF) taper. Do not buy a cheap fly line.
So, what should you buy? Most knowledgeable fly fishers would recommend a 5 or 6 wt. rod for a beginner...I agree. This is the most common size for most fishing situations for trout, bass and panfish up to several pounds. As you start to look around to buy equipment, you will quickly see that it is possible...actually easy to spend over $2,000 for just a rod, reel and fly line. Happily, that is not necessary although I do recommend that you purchase the highest quality you can afford. My first recommendation if cost is an issue is to purchase a combo starter kit with a rod, reel, fly line with backing from a company that really knows fly fishing. This will virtually guarantee you that the rod is properly matched with the fly line and reel and ready to cast. A few of the sources I can name with some confidence are Orvis (Encounter Outfit $169+), Reddington (Crosswater Combo $169), Temple Fork Outfitters (TFO NXT Black Label Kits $219), Echo (Base Fly Rod Kit $179). I know there are other less expensive choices and a google search will find them. I am hesitant to recommend them as I know nothing about these companies, their background or lack of background in fly fishing, etc. The really inexpensive ones are made in China and quality can always be an issue. Also, try to find one that comes with some sort of warranty.
If you prefer to purchase items separately and you have a limited budget, the place to "go cheap" would be on the reel as it is effectively just a place to store the fly line. This, however, changes as you start to fish for larger species and need the advantage of a good "drag" system.
A leader is what connects your fly line to your fly. They are typically made of a monofilament material typically either nylon or fluorocarbon and are tapered. They are heavier/larger diameter at the fly line connection end (butt section) and they get progressively smaller in diameter towards the "fly" end. Leaders are typically 7.5 feet to 12 feet in length. In addition to the length, leaders are also rated as having a specific "X" rating. The "X" rating is used by manufacturers to "size" its leader and tippet materials. Typically, leaders and tippets (see below) are rated from 0X to 8X. 0X is the heaviest and 8X is the lightest. This rating basically measures the diameter of the smallest end of the leader in "thousands of an inch" i.e. .003" for 8X and .011" for 0X. From this, you can closely determine the "breaking strength" as the larger the diameter, the stronger it is. For most leader materials, 8X has a breaking strength of about 1.75 lbs. and 0X has a breaking strength of approx. 15 lbs.
Tippet material is usually purchased on a narrow spool containing approx. 30 yards. Like leaders, the materials are usually nylon or fluorocarbon. The difference between tippet and leaders is that tippet is a consistent diameter and leaders are tapered. Tippet material is used to maintain the length of your leader. As you tie on different flies, a little of the length of the leader is lost each time. As the leader gets shorter and shorter over time, you add 2-3' of the appropriate size tippet material to keep the desired leader length. This is considerable less expensive than buying new leaders.
As you start actually fishing, there is probably more things you will want/need than a rod, reel and line. Among the most common are waders ("stocking foot" with separate wading boots or waders with built in boots). Stocking foot is by far most popular. Also, a landing net with a soft rubber net, a vest or other "pack" to carry all of the little stuff I have not yet talked about (nippers, fly floatant, etc.), rain jacket and more. Finally a good broad brimmed hat and good quality polarized sun glasses.