Kinda depends on what you want to build. I'd say going with either SOI or KLD is fine for now; except there is a sale in which case I'd jump ship straight away.
This. KLD and SOI should give you the cards to make a relatively wide range of aggro decks covering multiple colors that should be perfectly viable online.
From my past experience, if you have Origins fully unlocked you should be able to make a fairly decent Mono Red or R/W aggro deck that can beat the hard AI in well under 10 mins (should average around 5-6 mins to win). That's what I used to do and that should cut your capping time in half. It's not what I would call "fun", but it's kind of the price you pay instead of paying actual money.
This also. I would suggest doing this until you have most if not all of KLD unlocked. From there you should be able to make something that you can take online and be successful with (Rakdos Artifacts/Vehicles, Boros Vehicles, Gruul Energy, and so on).
If you take the time to look into which sets are worth unlocking first and play smart it can significantly cut down your grinding time.
I started Duels shortly after EMN came out (late July of last year) and still managed to easily hit rank 40 before the season ended, back when Xbox matchmaking was outright garbage. I was fully caught up on cards sometime around November and had enough gold saved up to buy all of AER the day it dropped. I will admit that I spent $35 on the game, because they had concurrent sales running for gold and a couple of sets (BFZ/OGW) and I wasn't going to pass that up.