Sometimes, rewards and incentive are motivational enough on their own. In a tabletop RPG like this where bonus exp, gold, or any other non mundane item gifted to a player for doing something that is largely required by the player as a means of character maintenance after each session and before the next is going to lead to unfair advantages when 1 or 2 of your average group of 5 end up majorly ahead in exp or currency or wealth measured in possessions (items obtained). Even Inspiration is something not to be handed out lightly.
So when rewards and incentives create imbalance? What's left is rules and regulations. My group always does their leveling at the end of each session, after XP is awarded, if said XP is enough to progress them to the next level. Sometimes our sessions run for 5 or 6 hours and everyone is too tired to do all the math and additions required for level up. No worries, they have a full 7 days to level their character! Seven days is plenty of time. There should be time in anyone's schedule over the course of 7 days to level up a character. Minds can be slippery sometimes, however, and reminders are required.
So how do you effectively go about this while respecting your players time restrictions and motivate them in the process? You make a hard rule. Session start time is Session Start Time . Character leveling up is the players responsibility. Anyone not sufficiently leveled up by the start of the next session 7 days later uses the character they have as represented on their character sheet. If they didn't go buy manacles and a chain, and the start of your session doesn't allow for shopping? If they didn't add all the nifty new things they gained for reaching level 4 and the session is starting? Well they're missing out.
You might say "Well that seems harsh, Airatome, where does the madness end!?" Well; you supplement that with reminders, if possible. Our group plays over skype so there is a consistent group chat always active. Whatever forum you use to bring your players together as a group has a method of messaging your group. So remind them at the end of each session to level up and shop. Remind them a few days later to level up and shop. Remind them the day before your next session to level up and shop. Anyone failing their responsibilities to keep their character sheet current after positive reminders and reinforcement is then stuck adhering to the rule of Session Start Time.
They can then level up their character if there's a break, or after the end of the session, and catch up to where they belong. Additionally, time allowing, you COULD have a soft session start time 1 hour before the implemented hard start time for those who need to catch up in levels and spend gold and such. This will not only give the people who already have done so time to make it to the session's actual start time, allow you as the DM to help any players who need it with their level up and HP rolls, but also allows everyone to start on an even note after the soft hour has concluded and the actual session begins. No delays. No giving out gold or items or Inspiration to those who should earn them in the game not out of the game because of a character sheet.
Regardless of the optional 'soft start time' being used, implementing a 'Hard Start Time' along with positive reminders after, in between, and a day before sessions should motivate them in a way that does not sow discord or advantages/disadvantages among the players; because after all is said and done, they DO gain the level they were missing; it's simply their responsibility, not yours, to keep their character current.
Generally speaking, if you reward people for things that are fun, it will gradually become less about the fun and more about the reward.
Personally, when we used XP per person, gaming was more focused on doing something cool with your character, as opposed to having fun and reaching the groups goal.
This is basic psychology, it's how the human mind works.
Now whether you want that is plain opinion. That's something you need to decide for yourself.
Best Answer
Inspiration
There is already a mechanic in the game that can be used to reward good roleplay (or whichever quality you want to motivate in your players):
Once a character has inspiration (multiple instances do not stack), they can expend it for a fairly major benefit: