There are plans to go mobile, but as of yet, that hasn't happened. They had started an alpha test on the mobile version but that's been put on hold for a bit.
As for what pack is best, Kinda depends on what faction you like the most, and which set has the better cards for them. As mentioned, you get packs for levelling, and I believe most of those will be from the core set, so chances are you'll want rise, Infestation, Ascension, or Order. You could also go with the collection pack which has cards from all the sets, but you'll also get more Core cards as well.