Your best way to reach 60 quickly is to change your quest settings to hell difficulty, select Act 2's quest called "Road to Alcarnus", and select the quest point titled "Lieutenant Vachem". Use your WP to reach the outpost, clear the cellar, let the prisoners out, and then kill all of the spawned mobs when you exit the cellar. Upon a quest completion dialog you will want to quickly leave the game and do it all over again.
You will gain a lot of XP/hr if you use this method. You can watch the following video on YouTube if you require more information: v=DiYnCa_-1X8
Find someone who has a decent dh with evasive fire-covering fire and have them run you through a3 and 4 hell (a4 gets thin at times). They will one shot anything on screen, elites may need another shot but you wont be in any danger as a leecher.
It will be hard to find someone since most good dh's are already running a3 and maybe tired of it. Maybe pay them with gold or something if you dont have a friend.
I always thought the fastest was the festering woods larger cave with all the skellies. Log in go there, get a massacre streak. Leave game. Log in and you start in cave. Get massacre streak. Rinse and repeat.
Obviously while wearing gains, xp gear and Rubied Helm
Okay so I took your advice out when I started leveling through 1-60. So for normal I leveled 1-23ish without buying anything from the AH. From there I got a friend to kill diablo on normal for me and I grinded out the 2 remaining levels to hit 25 and go to nightmare. So in nightmare I quested until I got to Act 2 Maghda killing quest (around 31-32) and I grinded that until around level 40.. Then I went on and did the Act 3 first two quests until I was level 50. From level 50 I had a nice level req bow that skyrocketed my dps and I could pretty much buy vit on all other slots (except cains set, I only used the one cains set through 23-60) so that I didn't die and had a nice DPS for hell. That's pretty much what I did while leveling my demon hunter.
1-25 regular questing until you hit 25, then you can ask a friend to kill diablo and go to nightmare
25-32 regular questing until you get to kill maghda quest in act 2 (BUY CAINS SET BEFORE 25!)
32-40 Grind the Maghda quest (Take the Kill Maghda quest, clear the packs outside of her little place and rescue the 8 prisoners for little exp boost)
40-50 Grind ACT 3 Quests 1-2 (Light the fires and the catapult thingie) Get someone to kill NM diablo for you.
50-60 IF you have good -lvl requirement gear go grind the 2 act 3 quests on hell, if you don't go do the festering woods or the Maghda trick.
Tips: Don't ever swap the cains set, it's good enough for all levels.
Also buying gear every few levels helps out a lot (Every 5-10 is enough if you're low on cash)
REMEMBER TO BUY A HELMET WITH A SOCKET AND PUT A EXP GEM (the biggest you can afford) It will make it substantially faster!
When on Hell I suggest getting a good -lvl req weapon for your class and pretty much stacking vit on other slots.
When doing the Act 3 Catapult quest, you don't have to help the first two catapults, you can just speak to the guys there and go lift the last one. (Where you have to actually do something)
This way took only 13 hours to level a Demon Hunter 1-60, so it's pretty fast, and if I ever feel the need for a another alt I will totally use this style again.