The players your team generates upon creation are rarely worth investing training on. It's especially true with team skills (stamina, free-throws, game shape) as there's no real tangible benefit to training these things on such easily replaceable players.
You can pretty much train any skills. 1-on-1, pressure, and passing are probably "best" for guards. Inside scoring, inside defence, and rebounding are probably "best" for big men. The best and most efficient salaried players often have high outside and inside skills.
It's probably ideal to acquire 2-3 solid trainees. I think nowadays you can get perfectly acceptable perennial allstar potential or higher 18 year olds for very cheap. As these players develop they can be key in helping you win and in addition are likely to greatly appreciate in value as you train them. At this point in the season you might be better off waiting to buy trainees until the draft at the end of the season. In the mean time, you can focus on arena expansions.