When rotation approaches, the 15 decks given to new players are updated, and every player receives one copy of every card they didn't have one copy of. However, this happens before the new set comes out. So no, don't expect free DMU cards to start with. Simply do your dailies and gather gold and get all those ICRs, up to six uncommons every day, with a % of them turning to rare or mythic. These ICRs won't always be from DMU, mind you, but they will always be Standard-legal (so from MID onwards). Along the way you get free packs from DMU while you progress in the Mastery path, and if you buy the Mastery Pass you get another 20 packs (with 4 or 5 of them being from DMU) and 10 mythic cards from DMU among several other things.

Now, to buy the pass you need 3400 gems and to get gems you need to draft. Drafting is considered the best way to grow your collection of any particular set, too, so is a win/win, but you'll need to read a little in order to not going 0-3 and feel you're wasting your gold. By drafting you'll get rares, packs and gems to buy the Mastery Pass.