The single most important attribute to train seems to be Plate Vision. Also, Plate Vision apparently determines how large or small the PCI (Plate Coverage Indicator) will be. Contact and Power is also important otherwise your player will be hitting the ball weakly. Begin by training against right-handed pitchers first since you’ll likely face more right-handed pitchers than left-handed pitchers. Later, you also want to make sure your attributes against left-handed pitchers are decent.
A good goal would be to improve Plate Vision, Contact, and Power to at least 60 or 70 for all players in the starting lineup. If your budget allows, try pushing plate vision up from 70 to around 80 or 90 for a few batters and you’ll likely see quite an improvement. For middle infielders you could probably get by with hitting attributes being lower than 60 and instead invest that money on improving their fielding attributes.
You may want to hold off on putting money into the Clutch attribute for those in your starting lineup but you may want to improve the clutch attribute for a couple players on the bench for pinch hitting situations. The clutch attribute ONLY takes effect during situations when runners are in scoring position (RISP).
The amount of training that you do depends on your budget and preference. You may want to spend some time training some attributes after each game or you can train your players all in one sitting. The cost of training is the same either way and the player’s aptitude (if it’s high) will still save you the same amount.
Reserve players will have a $2 million training penalty limit when you initially add them to the roster. Players on the active roster get $500K of training expenses per game. One recommendation would be when a starting position player is within 10 games of retiring you may want to start finding a replacement card and activate it to the roster as a reserve. Train your reserves as much as possible and then activate them to the roster to avoid over training penalties when your starters are within 1-2 games from retiring.
Try to avoid spending money on the “Per 9” attributes such as K/9, H/9, HR/9, and BB/9. these attributes tend to be more important for CPU controlled pitchers. If you throw the ball down the middle of the plate, the hitter is going to be able to whack the ball no matter how good your Per 9 attributes are. Focus on improving your pitches instead. Start by improving the break and control attributes and then work on the velocity. Overall, break and control seem to be the most important attributes for pitching. If you can get all of your pitchers up to 80 break and control, on all pitches (especially curve balls and change-ups), they will become downright nasty.