The latest rumors have the Phillies leaning towards Mickey Moniak, AKA Mickey Mo (though Maniak also seems plausible as a nickname). Moniak's hit tool may be a legitimate 70, which suggests a player you can put in the leadoff spot for the next decade and who will battle for batting titles. Rumors now lean heavily towards a hitter for the Phillies as the top pick even if it isn't Moniak.
Other names to watch for:
Kyle Lewis
Corey Ray
AJ Puk
Beyond the First, here are a few names we might hope slide to the top pick in the Second:
Jason Groome (insanely unlikely, but if he falls out of the top 10 picks, this becomes a realistic option)
Drew Mendoza
Alec Hansen
Alex Speas
Blake Rutherford (get very excited, there are rumors the Phillies are trying to float him to 2:1 and pay him Top 5 money. That would give the Phillies two guys with top 10, maybe even top 5 talent)
Now for some of the nuts and bolts of the draft. The First and Second Rounds, along with the compensation and competitive balance rounds A and B will be conducted today. The Phillies hold only selection #1 in the First round and will likely make their pick somewhere shortly after 7 PM Eastern. The Phillies Second Round selection is #41 overall and would likely occur sometime after 10 PM.
In general picks can not be traded, with the exception of the competitive balance picks (which is ironic since the whole reason picks can't be traded is it was felt it created an unfair balance toward wealthier teams who could afford to sign players cheaper/smaller teams couldn't).
On Friday rounds 3-10 will occur, beginning at 1:00 PM Eastern. Rounds 11-40 will occur Saturday starting at Noon Eastern and will blow past in no time (relatively speaking), as teams seem to take about 30 seconds to make each pick.
Each team receives a Bonus Pool from which to sign picks made in the first 10 rounds. The pools are based off of the slotting system for picks, so it's very dependent on which numbers of picks you have. The Phillies pool is $13,405,200. That gives the Phillies the second highest total in the league for total pool money (Reds have top money with $13,923,700). If you exceed that total on picks from rounds 1-10 you start getting penalized money and future draft picks. I won't bother with specifics, since it's detrimental enough no one has come close to doing it. After round 10, all picks from Round 11 on, need to be signed for $100k or less, however, if you have spent less than your bonus pool for the top 10 rounds, you can apply those savings to picks made in Round 11 or later. Any picks in the Top 10 rounds who don't sign, you lose their bonus money from your pool.
The Phillies will have a bit of a tough time getting overslot players at the top of Round 2 as the Reds and the 2 teams right behind the Phillies in bonus money all have multiple first round picks. The advantage the Phillies have is that ~3/4 of their bonus pool money is tied to 1 pick, while the Padres, Braves and Reds get their pool money largely from 4-7 picks. For that reason the Phillies only need to go underslot once to take advantage of their pool, while the other 3 teams need to go under on multiple picks to have extra pool.