PvP is, I would say, reasonably balanced. More balanced than, for instance WoW, which has always imho had balance issues. Blizzard tend to make huge changes to classes and they'll be constantly rotating from hugely OP to in the dirt. ArenaNet are constantly making smaller incremental changes to numbers to help balance builds and classes. There are certain weapons/builds that have historically underperformed outside of niche setups (turret Engineers, spirit weapon Guardians etc) but each class will have a range of viable playstyles available. Player skill and the circumstances of the engagement tend to be more of a factor than the classes at play, although there are certain builds that can prove troublesome for certain classes (fighting a good condi Thief as an Engineer is rarely fun). Generally though, I have no idea what my chances of winning are before picking a fight, because that greatly depends on how good they are at playing their build. Far less rock/paper/scissors than some games.
In sPvP everybody has the same equipment - while creating your build you choose which stat combinations you would like. In WvW, upscaling normalises equipment and player level to some degree, but an upscaled character will still perform as well as an optimised level 80 character. As you identified though, outgearing your opponent is not the way in which you set yourselves apart (thankfully, as that's just an awful means of determining the winner in PvP imho). The game can have a limited number of skills, so avoid playing something like a signet Warrior if you're used to other MMO's. This is part of the reason I prefer the Engineer class - with a three kit build, I have more abilities that I use frequently than I would while playing on WoW (especially since the ability pruning). Micromanaging all of their cooldowns and dancing between kits just adds an extra layer of fun to the equation for me.
Combat on GW2 is much more about controlling the fight. Generally, if you're in control, you'll win. I don't mean endless CC spamming to lockdown your opponent, but keeping your opponent at the right distance for your tastes, not allowing him to use his abilities in the way that he wants to, and managing your own health and conditions in the process. There's quite a lot to learn that will help you to succeed in the game and distinguish a skilled player from an average one. Understanding other classes builds and how their important skills are telegraphed (the interface isn't going to tell you, there are no UI enemy cast bars) is a big one. Thief at range starts moving his dagger hand? You have a split second to block or dodge. Mesmer raises his hands into the air and starts channeling? Interrupt him quickly and you've screwed with his invisibility. Ranger or Guardian raises his hands while you're trying to stomp him? You've got a split second to react and blind him or apply aegis/stability before he interrupts your stomp. Then there's combo fields. Capitalising on them in the right way can be enough to gain the advantage in a fight - especially if you and your teammates are taking advantage of one another's fields.
Classes are all reasonably well represented. You're going to see some of the usual MMO cliches, like a disproportionately high amount of thief players being bad, and a lot of them lurking around lower level play, but you'll frequently run into all classes. There are a lot of Warriors and Guardians in WvW, as it's generally easier to survive in zergplay while playing these classes.
Warriors and necros both fair well in PvP. There's no class that doesn't. The great thing about GW2 is that you can very quickly jump into hotjoin PvP and play against players who have zero advantage over you outside of their experience in the game, which is a good way to get a taste for a class and decide if you'd like to sink more time into it. I'd recommend looking into the Engineer class too, I often find that new people overlook it, but I am a little biased in that respect (played it since launch and definitely my favourite class).
Crafting is somewhat important. You'll need crafting to create Ascended weapons and armour, which are the best in the game. However, there's only a small drop from Ascended down to Exotic (the tier below). There's no easy money to be made through crafting, in honesty.
Light armour is used by Necromancers, Mesmers, and Elementalists. Medium by Thieves, Rangers, and Engineers. Heavy by Warriors and Guardians. You cannot equip equipment of a different weight class (Warriors can't wear light, for instance). It's really just a class-flavour thing. It doesn't affect your characters survivability - the depends on your trait set-up and the stats that your gear has on.