At what point should I stop buying Classic Packs? Is there a point where it becomes…pointless?
Also, which packs do these 3 cards come in:
Scavenging Hyena
Rat Pack
Pack Leader
These cards compliment each other so much it’s crazy. I have to have them!
Edit: Also, when should I start disenchanting cards? What criteria do i use to decide which to disenchant?
If you are not planning to spend too much, you can buy classic packs until you have most common and rare cards. The missing epics and legendaries, you can eventually craft them with dust. It’s never worth buying more packs just to get a specific epic/legendary.
Scavenging Hyena: Classic
Rat Pack: Mean streets of gadgetzan (It rotated out of standard a while ago, so you can only use it in wild)
Pack Leader (Only exist in battlegrounds at the momment)
Only disenchant extra cards. There is an option to auto-disenchant, you should use that. Don’t disenchant the cards that seems bad or that you think you will never use (Unless you already have 2 copies and get a 3rd). You can never know when a card that looks bad can become useful.
It can be a good idea to disenchant golden cards if you already have 2 non-golden copies. Golden cards gives more dust when disenchanted and they have no advantage over thier non-golden version, beside having an animated picture on it with a golden border. (Note that if you continue playing for a long while and regularely buy packs, you may regret having disenchanted those nice looking golden cards, so do it only when you absolutely want the dust right away)
Actually, Do not disenchant extra cards unless you have immediate need for dust.
Extra card can be subjected to nerf or HOF.
That’s a very good point, i never thought about doing that myself.
For OP: If you are a new player, you may not understand what it is about so i’ll explain just in case. (And if you do already know, well it might help someone else anyway). When blizzard either Hall of Fame a card (Remove it from standard before the yearly rotation, or simply removing a classic card from standard) or change anything about a card (increase cost, change the text on it, reduce health and damage, etc), there is a time window (not sure how long, one or two week maybe ?) where you get the full dust crafting value when you disenchant it. So if you happen to have a few extra of that particular card when it happens, the disenchant dust yield will be much greater than normal.
Now i totally regret disenchanting all my extra cards of this new Xpac, a few days before the shaman nerf 
I would actually add two addenda to this. First, there are a number of cards that are pretty horrible for game play except in extremely rare situations. A simple Google Search for “hearthstone cards that are safe to disenchant” will give you a good idea of cards that are probably not going to result in the nerf-bat change/HoF that you can get the maximum amount of dust from.
I know some people might disagree with me about this second one. Secondarily, if you want to play a particular deck and dusting the aforementioned pretty horrible cards to finish making that deck, (say, you want to make a Scavenging Hyena or two because you don’t have it and will fit really nicely in your hunter deck instead of waiting for RNGesus to favor you) make your card and enjoy playing the game. If you don’t have specific cards you are looking for, dust just sitting out there isn’t going to help you much so dusting cards prematurely isn’t going to help you much.
This is just my two cents.
As for your first question about buying Classic packs, stop buying them now. The cards are old and while there are some oldies but goodies in the mix, you are better off with the most current good expansion. Some of the time it is the current expansion, some of the time it isn’t as it depends seriously on what the new expansion has brought to the game. Look at the forums and do Google Search for ‘Top Hearthstone Decks’ to see how people feel about the current expansion and figure out what is best.
Thanks for the helpful replys people. I really appreciate it!
If anyone else has thoughts about this, please post!
\m/
You realize the actual game is nothing like Battlegrounds right?