In regards to the question of levels and time, I have two systems that I've used that both work very well for me and were well received by my players.
The first system is based around something WotC published in either 3rd Edition or 3.5 that allows players immediately increases in hit points and base saves. I tweaked it to the Age System to allow players immediate increases to hit points and mana (if mages), a maximum of 1 week of training per ability point, and a flat two weeks of training to learn a new focus or weapon group and class benefits. As an example, let's say character A has a 4 to Strength, and wants to increase it to 5, while learning the Axes focus. The ability increase would take a maximum of 5 weeks, with the chance to decrease time based on an advanced test. I set the TN at 14 with a success threshold of 10, giving the player the opportunity to complete his training in a mere two weeks instead of the full five. So, if his dice like him and he rolls high enough on the Dragon Die, in two weeks, the character could come away with a Strength increase, the Axes focus, and his class benefits.
The second system uses no rolling whatsoever and relies solely on roleplay, with bonus experience given for players that immerse themselves in the character and dedicate time to training in-game without prompting from the GM. Characters A and B both just hit level 5. Character A has been spending his downtime in-game to research combat techniques and training with willing NPCs, even going so far as to ask me if he can treat training with the local guard as a combat scenario and throw some dice while he does it. Character B, on the other hand, has relied solely on me to explain what is going on during his character's downtime. At the end of the session, Character A, having immersed himself in his character, has met a few NPCs, spent some time reading stories of fabled battles and legendary generals from Thedas' past, and generally just roleplayed like a champ. While Character B has sat idly by waiting for the next time I ask him to roll his dice. Character A is getting 200 bonus xp, while Character B isn't. After a few sessions like that, Character B catches on and starts spending more time roleplaying and less time "rollplaying".
On a moderately related note, I'll also share how I treat Specializations and the learning thereof. I've combined both systems in setting a minimum and maximum amount of time necessary to unlock the specialization while also tailoring the training and related quests specifically to the character involved and the specialization itself. Character A is interested in the Duelist Specialization, his character is currently in Rivain, spending time at a famous martial arts school learning the ins-and-outs of Duelist while becoming embroiled in a heated rivalry between his school and another school that will culminate with him dueling an NPC from the rival school in an effort to finally prove which school is superior. Character B, on the other hand, is currently bouncing between a traveling caravan of Dalish Elves, a group of Avvarian Hillsman, and a certain bard with a shiny crossbow, piecing together a combat style that will develop into the Marksman Specialization from the Set 3 Playtest. The character is combining all of the things he is learning about marksmanship with his training as an Antivan Crow in the hopes that it will make him an excellent sniper with a penchant for assassinations.