Tim Anderson hit lead off 4 games last year, hit .474 (6 for 19) with 2 doubles and a HR. OPS of 1.211. His second best slot was 6th, where in 12 games he hit .426 with OPS of 1.161. He mostly hit 2nd (65 games) or 7th (35 games), where he basically hit his seasonal averages. Here's one little tidbit. As the first batter of an inning, with 119 PAs, his slash line was .455/.470/.714/1.184.
Based on those numbers, I would hit him lead off to begin the season. He also led the team with 17 SBs, so there's that. Even though he only walked 15 times, you have to see what he can do at the top of the lineup. If he fails, the Sox have options.
Luis Robert would tend to be my pick to lead off once he's established. He didn't walk much either in the minors. 11 walks in 202 ABs in AAA. But the OBP was .341. And he can steal bases. But the key is that he's got power to drive in the bottom of the order guys, and he'll eventually be one of your best hitters, so give him the extra ABs.
Nick Madrigal doesn't strike out, but that doesn't make him a great lead off batter. It makes him a great batter behind someone with speed who is on base, because you can hit and run, and he can get deep into counts without fear of striking out. This allows more pitches to steal a base. Madrigal posted a .398 OBP in AAA over 28 games. That's certainly excellent. But his OPS is .792 compared to Robert's .974. Who do you want having more ABs? Robert or Madrigal? It's no contest.
Given this, here's my initial lineup to start the season, but only until Robert shows he's ready to hit better than Anderson.
1. R - Anderson
2, SW - Moncada
3. R - Abreu (whether he deserves to be here or not, this is where Renteria is going to keep him)
4. R - Jimenez (or could be Encarnacion). This is based off his ridiculous September when he mashed .340/.383/.710/1.093
5. SW - Grandal - he might hit 4th, but I keep him here for better R/L balance
6. R - Encarnacion (he hit better than Abreu last year - could be 3rd, 4th, or 6th)
7. L - Mazara (against lefties, I put Robert here, with Mazara's platoon partner 8th)
8. R - Robert - only until he shows he's ready to hit major league pitching, then he trades places with Tim Anderson
9. R - Madrigal - even though he should have a good OBP, his OPS will likely be the lowest in this lineup. This allows him to hit behind a speed guy where his bat control should have extra value. And if he gets on, he's poised to be driven in by the top of the lineup.
The reason I put 8, 9 and 1 together is those are the 3 fastest players in the lineup, so you can play speed games with them. You can also play the hit-and-run game at the bottom of the lineup with Madrigal, and with either Anderson or Robert in the 8 hole, you can steal and have them score with a single by Madrigal.