My advice would be to buy the most recent adventure first, to gain valuable cards that will remain in Standard for at least another year.
Once you own that and have played the single-player encounters, think about whether you actually enjoyed the experience.
If you thought it was fun, then yes, you should buy the other adventures while you still can.
To be fair this would be good advice if Karazhan was a good adventure. If you were to base the adventures on that one I think most players wouldn't even think of playing the others.
However back to the topic, I would say that if you want to get cards for Wild then it may be a good idea. Another thing to bear in mind is that with each adventure, you will know that you are getting certain cards, rather than spending your gold on 32 packs and hoping you will get certain cards, but most likely will get something you will rarely use in your decks.
Then there is the fact that if you want the heroic card backs you may want to at least purchase the first wing, so that when you get the gold you can spend to get that card back in your own time.
But that all said, if you are a new player it may just be wise to just forget about it. While it's good to have cards like this for Wild ( or even certain Tavern Brawl they can be very useful), they will not be good option if you don't even have a lot of the Standard cards.
What I will say is that if you are going to use gold, I would say consider your options. However at this point I don't think it would be wise to use real currency to get these adventures. After all, when it comes to Wild cards, it looks like Blizzard wants just to send them to the graveyard.