BuzzerBeater might be better described as being inspired by Hattrick.
Both training and economics work on a weekly basis, just like in HT, though in BB the weeks aren't coincident. The training week starts with the Saturday league game, with the training update on Friday based on the (up to) 3 games during the week.
Like in HT, training is only given to players who play in games during the week. It is restricted to the positions being trained (no osmosis training). Each of the training regimes trains multiple skills, though each has a primary skill which will improve faster. It is possible for a player to play multiple positions within a game, and this can have an impact on his training.
The "best position" shown on your roster is a suggestion. It is calculated as part of the training update, and can change based on training. What matters as far as the game engine and training is which position you use a player in.
A big different from HT is the game engine. BB is much more granular, with players having looks at the basket, and deciding to shoot or not. So instead of 10 scoring chances as in HT, you might have a few 100 in BB, with around 100 being reported as actual shot attempts. Players are treated as individuals in BB, rather than as simply part of a sector rating as in HT. Players play both ends of the court, and will use all their skills to some extent. Multi-skilled players are much more important in BB.
Potential is still somewhat of an unknown in BB. It was only introduced a season ago. Existing players were given an allstar potential (this is shown with an asterisk). This may be somewhat better than typical newly created players.
Players with less potential may still be able to reach skill levels that will have too high of a salary for lower division teams. While I'd shy away from announcer. "starter" ought to be able to get to a skill level sufficient to be a starter for your team.
Age is important for training. And you might also pay some attention to height. You might have a 6'3 guy who is your best center now, but he might not develop as fast as someone who is 7'2 (or vice versa for guards).
Game shape is pretty important. It is similar to form in HT, but if you keep your players in the range of 50-80 minutes per week, they'll be in pretty good GS (strong or prominent after a couple of weeks). Players don't go into a deep funk with atrocious GS in BB. The only time you would see that is if you had a player who rode the bench all season.
So you might need a 3rd game to get enough minutes, but you have to be careful about getting too many minutes as well. Once you begin training, you will probably want a scrimmage. Otherwise it is pretty hard to even train two playes in a position. And if you want to also win your league games, you probably don't want an 18 YO rookie starting - at least after you have played a season or two. Starting out, there may be newly drafted players who would be the best player at a position.