Hi, can you give more information ?
Which server do you play on, what class and spec are you planning to play ?
Depending on this the answer to your question differs vastly.
I dinged a Rogue at 80 last wednesday.
Hes now at 4650 Gearscore.
How fast you can get to gear depends on:
-Are you able to get starter Gold, of which around 10-20k is absolutely enough ?
If yes: Buy cheap but good boes of auction house, if your server economy has such. Spend the rest on GDKP, go for value items.
This also depends on the class and spec you want to play.
A rogue or boomkin is cheap to equip. Rogues weapons are highly uncontested, some of the leather aswell, and boomkin leather with spirit attached is basically only used by boomies and trees, making it amazingly cheap.
If no: You will need more time to gear.
If you are interested in how to make gold without swiping, quote this and i tell you (its easy)
So lets assume you want to gear yourself without spending Gold.
Then it still depends on your server, your class and your spec.
Playing a sought after support spec like boomkin, shaman or shadowpriest allows you to get groups for content way above your gear, just by being a player that brings the spec the group needs at the opportune time.
Being able to heal can also be of help, especially at offtime Naxx fullruns, where healers can be severely lacking.
Due to the majority of players being meta slaves, Heroics and Heroic+ should be the last thing you look for, if you want to gear up your character.
Even if you got no issues getting into groups with low gear, which on some servers actually is the case, the meta dictates that anything that is not daily HC+ and a skiprun is unworthy of time spend, so its a very bad way for getting gear.
PVP is also a nice and easy way to get some decent pve gear.
Also try your luck with Emalon, if you play one of the classes having it hard to get a spot make your own group, all it takes is some time in the lfg tool ninjainviting everything that pops up which you still need for your specrun.
If you happen to play something that is sought by 95% of every emalon group, just enter the tool and get instant invite. Nobody cares that you have low gear there.