How does everyone approach this? I'm still learning. If a team has 4 good Setup A guys, and all are at 100% health, in your experience, does the best player always get the call?

the sim will pull what they deem the best of that group, which many times lines up with what I believe, but not always.  Your inning available setting also effects this.

I think - THINK - that in my experience, if you leave them all at SuA, with the same innings, the sim will hold the overall best one to close in the 9th.  So if you'd rather that guy come in earlier, you have to set things up to make sure he does.

Not saying this is 100%, but that's what's happened to me.

The best player for the situation gets the call. I'm not sure how deeply the sim searches situations, but batter/pitcher splits would seem likely along with some consideration of outs/runners and batter's strengths. I often set everyone in the pen to SUA and the sim balances their usage somewhat. If it were just the "best pitcher" one guy would be overused and one never used. I usually have to Rest the best of the group once every 15-20 games.

I haven't noticed the best being held for the 9th, but I also go through and make all the SUA available in any inning. If you don't manually change the Player Settings it might carry over the most-recent closer's available inning as 8 or 9.

In my experience, my best guys get used first/more often.   I could post examples but I'm lazy.    Click on my Mantle team(A/S break) and you'll see this.

Matt Christensen	43	0	0	0	5	1	11	13	72.0	66	25	22	7	19	61	.237	.286	.360	1.18	2.75
Don Benjamin	36	0	0	0	0	1	1	2	37.0	32	12	11	4	11	23	.229	.289	.343	1.16	2.68
Freddie Larish	33	0	0	0	2	4	7	7	42.2	27	7	7	2	11	31	.182	.253	.236	0.89	1.48
Vic Benitez	25	0	0	0	5	0	2	3	30.1	18	5	5	0	18	25	.176	.309	.196	1.19	1.48

This first three have been SuA all season with 6th inning availability.   MC was put on the DL a couple of days ago or he'd have more.   And, IMO, the number of appearances equates to skill level.   Benitez has been SuB until MC got hurt.

A warning about SuB: I set my worst reliever to be SuB and he has the most IP out of any of my relievers. Of course, those IP are probably in lower leverage situations, but I don't like it. I have a good offense and I think this loser SuB is costing my team chances to rally late in games. When I think the SuB might be a good strategy is if you have 2-3 equally weak relievers you want to use more during blowouts.

Any thoughts on the LH/RH specialist role? It doesn't seem to be a popular strategy from what I can tell.

It's never worked very well.   They seldom get used.

My third best RP is used for SuB.  I typically make him available in the 7th inning.  SuA is the second best RP and is slotted for 8th inning.
I use LH or RH specialist when they would not be in the majors if they faced both RH and LH batters.  Typical differential on splits is more than 10.