I played since last April I think, basically just missed the first 2 or so "official" months. I played on Casual almost everyday until I finished a daily. The end of the month I would play Ranked enough to get to rank 20. By the time Naxx came out (first wing was free btw), I was able to drop gold on the whole thing. I didn't play much since then, just at the end of the month to get rank 20.
I started playing more frequently this past May (almost everyday). I only purchased the first wing of Blackrock and currently am at ~4200 gold. I have yet to try Arena (my first free try is in use and am the class selection screen) and never bought cards or crafted. I only use Classic/Naxx and the few BRM cards despite only opening 6 card packs ("expert"/classic). Check outbasic "Sheng" decks for ideas. many gimmicky decks aren't viable despite making people pissed when it works.
Keep in mind there are now 3 "beginner" type of quests instead of 2 that all new accounts have access to that reward classic packs (complete a game, get a class to level 10, win 5 practice games which is new). Playing a game on iphone, ipad, android phone, and android tablet will get you a pack for each device as well. There is also a daily to spectate a friend winning a game.
I was able to end May at rank 16 (could not hit 15 and highest month before was 18 when only playing end of month). Rogue got me the most progress. I also finally tried Hunter in Ranked. I made a basic face deck using just basic/naxx cards. Games are easy if the opponent doesn't have many taunts.
I'd say up until rank 18 (middle of the month on), more than half of the players have no idea what they are doing (coining turn 1 to use their power or dropping a minion with valuable effect which can obviously be killed on opponent's turn).
I always love winning against people dropping Rags, Jaxx, or whatever op Legendary mininon they felt the need to craft (or entire "pro" deck). Oh and Dr. Boom too. That can coming back when "behind" in hp. Lots of players go face for no apparent reason. Sometimes they take out a minion when going face would have been better too.
I think knowing which low cost minions to kill on sight is very, very important (Knife Juggler, anything that is card draw, stuff that buffs everyturn etc) as well as what the main class spells are.
Grinding for gold isn't as bad as I thought. Ideally people shoud reroll their quests properly. Complete 60/100g quest (and spectate) the day it appears. Reroll all 40s, making sure to do so right BEFORE it is completed. This ensures you won't accidently complete a 40 when trying to do a 60 quest. Note that the 100g can be done in practice mode.
Anyway let's just say 45g a day for the "daily". 6 wins a day is not too bad for 20g (3 wins ->10g for max of 100g from wins a day). That's 65g a day. if you play every day a month, thats 1950g. If you actually put more than 60 hours a month (2hrs a day should be enough to finish quests), that's more gold. An extra case (30 wins in Play mode a day for 100g), that's 3000g a month not factoring in quests.
Arena doesn't seem that "hard" to get 2-3 wins (3-4 is the target to go even) so I suggest watching videos on the draft process. that is the mist desriable way to expand card collection without spending actually money. Again I haven't tried it as I still don't feel that I have been exposed to the majority of viable cards yet. Also I'm ocd in the way I play games so whatever.