Hello and welcome to GW2!
Glad you started playing this game, it's actually fun! I myself have a level 80 Mesmer decked out, and been playing for quite awhile (along the same timeline as Capt). My best advice for GW2 is to complete your "Heart" events, and events in general, to include your personal Story line since they give the best XP.
You can also do WvW (World vs. World) but I would stay away from it until you're up in the 70-80 range. This is because although you do "up" level to 80 - your gear stays the same (i.e your level 80, but your gear is level 10). You'll be smooshed in a heartbeat lol...
Necromancers I'm assuming are fun to play with, and I've played against them in my WvW/sPVP (structured PVP) and let me tell you, they're no easy class to take down... lol
As for buying dye's - I agree, the common (blue name colored) one's are cheapest and start off with those, if changing your color scheme is your thing... good thing about dye's is once you "learn" it, it's always with you.
On the weapons/armor - I wouldn't worry too much about this while you're leveling, each "Heart" event you complete has a "Karma" vendor that will likely have weapons/armors for sell via the Karma you've earned throughout your gameplay. Armor and weapons really only come into play once you're level 80. From there I would highly recommend you go all out "Exotics" (orange).
Dungeons - Highly recommended you complete these at end-game. The game world has several different types of Dungeons (Citadel of Fire, Twilight Arbor, etc...) that you can complete. Each dungeon however, will reward you with it's own specific type of "token" that is used to essentially buy for exotic Armor/weapons and misc equipment/items. Different types of stats are associated with a specific dungeon, for example, if you want +power +crit.. you would do Citadel of Fire. If you want +magic find (MF) you would complete Manor.. etc etc..
In the end, highly recommend you enjoy the game with however and whichever type of class you want to play with. Don't get bogged down on what stats (skillpoints) to level, or whatever the flavor of the month is. There are more than enough skill points in the world than you need!
Enjoy - and if you need ANY help feel free to message me ingame (Zero To Hero). I'll be more than happy to assist you, perhaps with a small boost of anything needed.
Edited: I guess they do upscale your armor - but you still do very minimal damage compared to level 80's (which mostly all are). Just fun to do though, so go try it out!