Demon Hunter was nerfed within two days of its release, but the class remains strong, it is just more in line with the other classes now.
However, for budget players the nerfs present a problem because the prevalent Demon Hunter archetype on the ladder is aggro, which requires two Legendary cards and two Epic cards from Ashes of Outland, as well as Frenzied Felwings from the Galakrond’s Awakening adventure.
I have built and playtested a Midrange Budget Demon Hunter deck that can be built without any of those expensive cards and that can succeed on the current ladder.
Budget Demon Hunter decklist

Deck code: AAECAea5AwTJugPMugPUyAPVyAMNh7oDi7oDvbsD17sDnLwD4LwDusYDx8YD2cYD18gD98gD+cgD/sgDAA==
This list overcomes the lack of expensive cards by using the cheap power cards still available to the class: Priestess of Fury and Altruis the Outcast.
Because you are inevitably slower than the expensive aggro deck, you need healing to succeed in the mirror match. I have found that both Aldrachi Warblades and Ashtongue Battlelord are necessary to overcome the impressive damage numbers the aggro deck is capable of.
I also still use one copy of the nerfed Imprisoned Antaen. While it is the weakest card in the list – and there always has to be the weakest card – it is necessary for a budget deck to provide the deck with some more overall damage for slower matchups.
Consume Magic can both help to defend against Questing Adventurers and attack through Taunt minions.
Budget Demon Hunter mulligan

Your mulligan is similar to the full-cost lists because the early-game minions are largely the same.
Always keep Battlefiend and Umberwing.
Keep Crimson Sigil Runner if it is in a position where you can activate its Outcast effect, either as the left-most card or if all the cards to the left of it are early-game cards that you also keep.
In slower matchups, keep Raging Felscreamer and maybe even Priestess of Fury. You can also keep Satyr Overseer with Twin Slice or with Umberwing.
Against aggro, keep Eye Beam and Twin Slice.
Budget Demon Hunter upgrade path

You can easily upgrade the list to my full-cost Midrange Demon Hunter that I have been playing in Legend: replace Consume Magic with Kayn Sunfury and Imprisoned Antaen with Metamorphosis.
If you want to upgrade the list to the most popular aggro lists, you also need Frenzied Felwings and Warglaives of Azzinoth, so the full midrange list is a good intermediary step towards the aggro lists. There are also some aggro lists that cut the Warglaives, but they absolutely need Frenzied Felwings to work.
At this time, the aggro lists are still being developed and the rest of cards vary, but none of their other cards are expensive. Whether it is Questing Adventurers or Furious Felfins or Frozen Shadoweavers, the remaining pieces cost only a little dust once you have the adventure cards and the Warglaives.
Budget Demon Hunter tips and tricks
The Outcast mechanic is important to master. You get the bonus effect when the Outcast card is your leftmost or rightmost card when played, so try to think a couple of turns ahead on how you will use cards from your hand to position your cards accordingly.
Altruis the Outcast is your most powerful card. Sometimes you need to use it for early tempo, but usually, you want to go for a huge turn in the midgame, preferably with some cards discounted by Skull of Gul’dan.
The main use of Raging Felscreamer is to discount Priestess of Fury. Felcreamer on turn four followed up by Priestess on turn five can be devastating for the opponent. Secondarily, you can use it to discount Imprisoned Antaen, and sometimes just the tempo from discounting your smaller Demon can do.
Twin Slice is an important card. If you do not find a weapon, Twin Slice can activate your Satyr Overseer or Glaivebound Adept without spending mana. It is also great with Altruis the Outcast. Do not spend it too hastily, although sometimes you just have to use at least half of it to remove a Battlefiend early.
Budget Demon hunter gameplay video
Finally, here is a gameplay video of the deck. It showcases how to pilot the deck and make the most out of the Outcast mechanic and Altruis the Outcast.