Only if I get the sense you’re doing it for the wow factor do I tend to shy away from these, but in general I’ve seen a few of these types of characters (DH and Dragon) done well. If you (OP) decide to head this route with demons make sure you are well acquainted with who and what those demons are, what role they play within the legion and at what power level they generally rank. There’s nothing wrong with binding with a Pitlord, just be certain you do your homework and give it and your character their due justice. Remember to work in a few (or a couple) significant flaws as these will help ground your character and make them relatable to other RPers.
Though I would still advise to shy away from higher tier demons. You’re going to have enough hurdles to deal with as a Demon Hunter. A DH bound to a Pitlord will only add complications, imo.
Pretty much what I and Livi mentioned above. Start with the before your Demon Hunter was a Demon Hunter, they were Sindorei or Kaldorei. Focus for a minute on what that meant to them. Every Demon Hunter chose to follow their path out of vengeance or power-seeking, or a combination of the two, but think for a minute about how this motivation applies to your Elf. What did they loose? What/why were they willing to sacrifice what was left? Having a general sense of these going forward will help flesh out your character.
Don’t forget to work in a few character flaws as well. Even just one key flaw can go a long way to keeping your DH grounded, relatable, and interesting as a character.
I’m just offering my 2 cents here. By no means am I an expert, but these are things that have worked for me, and I’ve seen them work for others.
For my Demon Hunter, I’ve focused on why Vesthi gave up what she did. I made her an ancient Night Elf to give me more than enough time to develop her tragedy long before she followed Illidan into Outland. She has a lot of old wounds and baggage to deal with, vengence on the demons that destroyed her and stopping the legion’s march were only the first steps for her. As a character she’s still got a long road ahead of her, and so when I RP Vesthi I focus on those matters.
Right now in my writing for her I’m focusing on her sense of patriotism, her love and pride for her people. Where she wasn’t terribly concerned about the faction conflict before the burning of Teldrassil pulled her into the fight. Her major flaw in this is that all the fanaticism and fervor she once focused on the Legion is being turned toward the Horde, and it’s causing some serious problems for her.
That’s just my approach for this expansion.