This depends on time available and skill.
Infinite arena is considered the best way to get cards and dust. However, even assuming you can consistently get 7+ wins, it's bad for actually earning gold. 7 wins typically earns you between 150 and 180. If you don't factor in the free pack and the bonus prizes, that's 10 games, drafting time and risk for less gold than the 3 games/10g.
8 wins isn't much better, 9 is actually worse (you get more cool stuff) so you'd really need 10 wins in a reasonable number of those 7+ runs for it to be worthwhile.
On the plus side, infinite arena is actually infinite. There's no cap so you could play 24/7 if you want.
Quests are the most time-efficient method. Assuming you are capable of using at least 5 classes, you can reroll everything to get Domination quests and get 60g most of the time. Assuming a 50% winrate, this takes 10 games to earn 60g+20g for the 3 wins quest if you play an extra match.
Timewise this would take about an hour and a half, assuming just under 10 mins/game.
Once you've beaten your quest, your only remaining option is the 3 wins quest. This is slow- earning you 10-20g per hour. However, you can use it to supplement the quest rewards. The method above earns you 540g per week (80/day) so winning another 6 games pushes this to 100. This is enough for 700/week or enough to buy naxx wings as they are released.
Since you can play whatever deck you want here, this may be quicker than winning the quests. About an hour, probably. In total, that's two and a half hours a day.
So, to summarise, reroll your quests to 60g, beat those then beat the 10g/3 games quest to make up the rest of the money you need.