Short answer: it's not really worth buying or crafting armour and weapons until you're level 80 and plan to keep your gear.
Stats from items dropped as you level up should be good enough for general PvE unless you plan to play "at the edge" of your level. If your gear isn't so good, just explore and complete maps 5-10 levels below your own and don't get ahead of yourself in your personal story.
If you're worried about looks before you get to 80, use transmutation stones (from map completion or dailies) to transmute items with skins you like (you can always preview what it will look like) onto your current best gear. Once you hit 80, those transmutation stones will be worthless (to that character) anyway since they only work on gear up to level 79. Keep gear you like, learn to manage your inventory and your account storage, sell or salvage gear you don't like. If you played Guild Wars (1), the Hall of Monument skins look decent enough and are free, you don't even need transmutation stones.
Once you're finally at level 80, it's worth spending a bit of time buying or crafting at least Masterwork (green) gear - I know you said you're more interested in drops but you might just have to get over that. (Plus, remember that what seems extremely expensive when you're first at level 60 is chicken feed by the time you get to 80.) Or, if you're in a decent guild, ask your guildies if they can donate some spare gear. If you're really against buying/crafting, run some events down in Orr (e.g. the Plinx chain of events is great for this), you'll be visiting merchants quite frequently to make space in your inventory from all the drops.
Initially, you'll want to ignore the stats and go for the highest armour you can get your hands on. After that is when you want to inform yourself about specific builds that interest you and what sort of gear works best with them (e.g. Berserker for a warrior, etc.), and set about obtaining each piece. Aim for rare (yellow) items first, then exotics (orange). One other recommendation is to go for magic find gear (e.g. explorer armour with opal orbs) first, and wear that to get better drops. As you get them, don't be afraid to sell good gear you don't want on the trading post and use the money to buy gear you do want.
An easy way to a) get nice-looking exotics, b) make lots of money, and c) get karma and experience is to run dungeons. Just make sure you only join groups willing to take along someone still improving their gear and expect to die lots until you've improved your gear and figured out how best to play each dungeon. Citadel of Flame has most groups running it (use http://gw2lfg.com) and arguably some of the best-looking gear (trade dungeon tokens you get in at the appropriate trader in Lion's Arch).
So to sum up the long answer, there's no single, cheapest, quickest way to achieve what you want. It's a process of continually improving your gear over time, or you'll have to farm money and buy from the Trading Post or craft your own. Even if you're very lucky and get the drops you're looking for (more likely, though, "these are not the drops you're looking for"), you'll need to invest some money in specific runes for specific builds - it's very hard to find all the right runes by yourself. It comes down to how much time and how much money you're willing to invest.