There are different degrees the definition of Apo, depending on the specific application in mind, or alas, the marketing advantage perceived in calling something only modesty improved that. But for all practical purposes, nearly all modern LF lenses (from the 70's onwards) are so well color corrected for general photography purposes that it's a non-issue. Multi-coating is a somewhat different subject, only sometimes related, and again, basically a non-issue with modern LF lenses. That doesn't mean older lenses are bad, but just gives a general reference point. But no ordinary "apo" LF lens is equal to the graphics standard of Apo. No need to go into that topic here - it's complete overkill unless you are intending to make huge exceptionally precise color enlargements.
But in theory, yes, apo correction helps even black and white shots too, especially with respect to acute performance with a variety of contrast filters, and not just some. That's more a problem with smaller formats where greater degrees of magnification in enlargement are generally needed.
But as far a marketing bait goes, the German brands of Rodenstock and Schneider decided at one point to affix the Apo designation to their general purpose lens upgrades, while Nikon and Fuji didn't, even though those Japanese varieties are every bit as good from the same time period. So don't let a mere marketing label fool you.
Now as per film choices. That is your limiting factor at this point. No lens is going to make HP5 look sharp at significant enlargement. It's lovely film, but I don't like shooting it in any format smaller than 8x10, and even then, never enlarging it greater than 2.5X. FP4 will hold far more detail, but doesn't have as fine grain as a number of other films. Tonality is generally more important in LF work anyway. But you haven't even told us what format you work in, or how big you print.
And there are other variables involved in getting optimal acuity all the way from shot to print.