System suggestions please?
Gurps. Each level is a different point value. Start off small, maybe 25-50 points. Assigned training points during the training phase to cover learned skills (don't forget a list of electives).
There are a couple obvious skills to be learned on board the ship, during the travel phase, which can assigned, as well. Shipboard job assignments translate into more skill points.
And, of course, the Colony phase takes care of it self, as you don't need ways to boost character levels (point totals), anymore.
Gurps calls 200 hours of training equivalent to a point, so a year's schooling is about 10 points per 50 weeks at 40 hours/week. There are rules for somewhat more intensive training, if you want more skills in a shorter time period, but a bachelors' degree is a 4 year course, for about 40 points. This is 40 skills at basic training, or fewer at higher levels.
There are also rules in the book for training time on the job into more skill points for a higher skill level, which might come in handy for the shipboard portion, if you're mainly looking for an experience boost
Both the training and ship phases can also add actual experience points to spend on whatever the character wants,a s well, if you want to play out portions of one or both phases. And,f course, that will be what you use for the final phase, which is likely the main game.
I've done this a couple times using Gurps, although I used cold sleep so the ship phases was less of a factor for me, save at the very end of the journey.
I've not had great luck, but that could be me, or it could be I used slowboats, and no FTL comms, so it was a one way trip. Colonizing a planet isn't that much fun unless it's a weird planet. Just saying. Otherwise it's most a job, not an adventure.