Want to draft Dominaria? That's easy. Want to draft Dominaria well? That's a bit harder. Here are the cards you should be looking for, in roughly the order you should be picking them.
The Best of the Best
These are the best of the best, and are the cards you hope to see staring back at you when you open a pack of Dominaria. Note that Icy Manipulator and In Bolas's Clutches are on the list, which makes this one of the few times that uncommons have made it to the highest tier. They are there for a reason, and will take over any game in which they survive (while also not being very easy to kill). Cards in this list have a huge impact on the game, don't cost tons and tons of mana, and will often help you get back into the game when you're behind. If you're lucky enough to open one, go nuts.
*Yargle may not actually be in this tier, but I couldn't help myself. It's more of a mediocre playable, so don't go slamming it quite yet.
The Best of the Rest
These are great cards that you are happy starting with, and they all rank above the common/uncommon removal spells. Most of these are threats, and lots of multicolored cards live here. Note that powerful cards like Yawgmoth's Vile Offering still take some work to enable, but the payoff is huge. Likewise, taking a gold card first commits you, but these gold cards are worth it.
Good First Picks
This category kicks off with the best common removal spells, and is a mix of good uncommons and the best commons (plus a couple reasonable rares that aren't quite bombs). These go from above-average first picks at the top to almost dead-average first picks at the bottom. If you start with one of these, you aren't too committed—you can move into other colors if better stuff shows up.
These cards are all fine playables, but as first picks, they are lacking. You don't want to start off a draft here unless you must, though these are all cards I'm happy putting in my deck at the end of the draft.
Hopefully this helps you kick off the season, as untangling a new Draft format is always a ton of fun. As usual with Draft, it's best to prioritize colorless or more flexible cards early, but some of these cards are too good to pass even if they're multicolored.