Wow, this is a BIG question.
For me, it depends on the player and how I am wanting to develop him, but I will try and answer in a logical thought-process kind of way, firstly, remember that the attribute values you see on his Overview card are actually measured to two decimal places, so a player with an attribute at 10, can be anywhere between 9.50 and 10.49 so 'rapid' increases may only be a rise of .01
Second, first team playing time gives a little boost to the attributes used in the position/role/duty he played with - so if you have a promising Poacher, playing him as a DF, while possible, won;t improve him as fast. Important to remember that he will only get a boost if he is on the field long enough to receive a match rating - About 15 minutes. The longer he is on, and the higher the rating the bigger the boost - although still only small and measured in the decimals.
Mentoring can be valuable as well, mentoring 'on the pitch' helps with PPMs and some attributes (determination/work rate etc) and 'off the pitch helps with determination and personality.
Now, remember those points when we talk about loans, but, looking at a youngster I would first decide what I want him to be when he reaches the first team, so, what position and role would fit my tactic. I then look at the weaker attributes he has for that role and see which positional training will improve those. Remember to keep an eye on the physicals & mentals as well, these improve quickly when young - so if the player has Poacher set as his best position, training him as a CF might produce a more-rounded Poacher for your first team. Any attributes particularly weak can be trained on individual focus.
Now, if you want to give him a run in the first team, remember the attributes that will be helped - do you play him as a CF or as a Poacher to fit your tactic? That is entirely up to you and depends on how he is progressing with his in-house training.
On to the loaning issues, this can be a fantastic way of developing youth if done properly - David Beckham's professional debut was for Preston North End, and he has publicly said how valuable playing for PNE was in his development - so, there a few things to look out for. Most important to remember though is that you lose all control over his training, what attributes are worked on and what role/duty he plays, so loaning a good 'un might not be the best thing, especially if relying on Mentors - they have no influence if the player isn't at the club.
Check the players report tab and see at what level your backroom team recommend he is ready for - do not ever loan to below or above this level! Below, and he won;t get pushed enough to perform, attributes get little or no boost at all, above this standard and he either won;t get playing time or won't be able to perform and lower match rating means less attribute improvement.
So, you get some loan offers from clubs at the level he should be playing at, look at their training facilities and coaching quality - is it good enough? Should be better than yours, on a par with yours or one level below. The Youth facilities have little impact as he will be with the first team.
How is the loanee club performing? Playing at club that is pushing for promotion or competing at least Top 10 or top half is more valuable than playing for one struggling at the bottom of the league.
What Squad Status are they offering? I never loan a player out at less than First Team status, he just won;t get enough game time at anything less. You can check out the loanee club squad screen to see who he will competing for place with as well. If possible I will push for Key Player status, but happy to settle with First team.
So loaning is one of the best ways to improve the player as long as he is placed at the right club, is played in the right position and is getting regular games - at least more minutes than you could give him - BUT you do lose all control over the development of the finished player, so make sure you have trained him properly first. If he is not performing at all, or not getting game time, recall him and take back control over his development.
I should also note that you should ONLY loan to clubs in 'Playable Leagues' - non-playable leagues don't actually run the full fixtures so he will only see the benefits of match time in a playable league where all fixtures are run thoroughly and he gets actual minutes.
So, to the question (
, reserve team fixtures do little to improve the player, 'meaningful fixtures' are what counts, so league games & cup games in the first team, basically the same fixtures that matter to your Key Player/Firsts/Rotation players when they moan about playing time.
