Much like weapons, armor has a set of stats associated with it which speak to how well it will protect, how well it's made, its hindrance, etc. Let's look at the most common set of leather armor in the realms, which would be Wolf Clan leathers. These are pretty much the standard for leather protection:

    The leathers are leather armor.

    The leathers look like they offer protection for the following areas:

        right arm
        left arm
        right leg
        left leg
        chest
        abdomen
        back

    You feel certain that some sable leathers appear to impose high maneuvering
    hindrance and offers:
        good protection and fair damage absorption for puncture attacks.
        good protection and fair damage absorption for slice attacks.
        good protection and moderate damage absorption for impact attacks.
        fair protection and fair damage absorption for fire attacks.
        fair protection and fair damage absorption for cold attacks.
        moderate protection and fair damage absorption for electrical attacks.

    If you were only maneuvering in some sable leathers you could expect to be
    unhindered.

    You are certain that the leathers are moderately strong, and are in pristine
    condition.

    The leathers are moderately soft.
    The leathers feels pretty heavy.
    You are certain that the leathers are worth exactly 1875 kronars.

This format is often abbreviated as such: g/f g/f g/m f/f f/f m/f for simplicity. It's also sometimes noted as g/g/g/f/f/m with fair absorption which I find a little more obfuscated. The scale for the values is:
none, poor, low, fair, moderate, good, high, great, extreme

Protection:
The protection value (being the 'good' part on puncture for instance) is probably the most important value to keep in mind when choosing armor. As your ranks increase, the protection value works with the ranks to provide the overall amount of damage reduction when you take a blow. So, with more ranks in an armor skill comes better protection. If an armor had poor protection you probably couldn't expect to grow with this armor, even though it did have some intrinsic value for protection, known as absorption, talked about next.

Absorption:
Absorption is the built-in protection of the armor, the part which doesn't increase particularly with ranks in armor skill. It's simply how much of the damage the armor will take when anyone wears it. In the case of an armor like leather, absorption is almost always quite low, meaning that most hits that do manage to get through and have ignored your protection value are going to hurt. Generally speaking younger people are often best suited with armor with somewhat higher absorption and can later grow into better protecting armor.

Hindrance:
All armors impact maneuverability and have a value associated with this, which is its hindrance. Being hindered effects an entire host of skills, most of which are combat, such as evasion, the damage dealt through your weapon, your armor skill itself, but also non-combat skills like swimming. Early on, it's important to pick armor which isn't terribly hindering and there are several options out there, such as supple hunting leathers sold up in Riverhaven. Another important note about hindrance is that the more you're hindered, the better you learn, which seems a little backwards. Later in your career, you'll find that wearing less hindering armor will actually cause you to learn leather armor more slowly. In either case, you're still gunning for very low hindrance, either insignificantly hindered or unhindered.

Construction:
The construction value dictates how much damage the armor itself can take before it needs to be repaired. Generally speaking armor will take some damage over its lifetime, but even some of the worst constructed armor will hold up for a long time. There are a certain group of critters that simply tear armor up, such as granite gargoyles and so you may be paying a visit to the leather repair shop more and more often as you get older if you don't move to armor that's at least moderately strong. Also, dying tends to cause damage to armor, but for some bits of armor it's simply impossible to get really good construction, such is the case for leather hand and head gear or even chain hand gear.

Appraisal value:
The amount that the leathers cost means nothing except how much it's going to cost to get them repaired. The leather repair shop notes the value and figures it out in their estimates, so owning some really fancy fest leathers that don't protect any better than store bought isn't always a good idea.

Early on, I suggest that rangers get the supple hunting leathers from up in Haven. They end up with stats like m/m m/m g/m and aren't as hindering as Wolf Clan leathers, as well as only having a cost of a few gold. Racial hunting leathers sold down in Shard are probably the all around best choice but can run close to 5 plat dokoras and that's simply too much for most people starting out.
Once you've moved up a little, perhaps after about 70 ranks of leather armor skill, I suggest going to the Wolf Clan leathers. They'll be heavy, but the protection gains will start to be worth it. This is also the time when you start moving up to critters which will hit fairly hard such as snowbeasts and soon enough granite gargoyles. As for head protection, the leather mask in Shard is a good one and only costs a few silver while protection head, neck and eyes. Reinforced gloves sold in Crossing will do just fine for leather hand gear. The falconer's gauntlets on Ratha are another popular choice, but try not to get ripped off by people selling them for more than a gold.
If you're beyond even those, say in the mid-100's in leather armor, you certainly can't go wrong with tanned leathers. A couple of rangers sell good sets of tanned leathers which will provide somewhat more protection, but the cost is quite high, usually 80 or more plat. I suggest doing your research first though.