S.,
In my opinion, 3 months is not too young ... we started at 4 weeks and our son was sleeping through the night and at all scheduled naps by 8 weeks ... With my next child I am starting the day we come home from the hospital!
My son is 20 months and is still a rock star sleeper, and a very happy, well tempered baby! They like to know what to expect next.
Here is the schedule we used from 2 months - 5 months ... Then we modified it again at 9 months, 12 months, 15 months ... You will know when it needs to be adjusted for you and your family. :)
7:00 am - Wake, eat
7:30-8:30 - Play (This does not mean that you have to be constantly stimulating your child ... it can be that they are laying on a playmat, tummy time, watching you fold laundry, etc.)
8:30-10:00 - Nap (Even if he did not sleep the entire time, he stayed in his crib. If he was crying ... it was not time to get up)
10:00 am - Wake, eat
10:30 - 11:30 - Play
11:30 - 1:00 pm - Nap
1:00 pm - Wake, eat
1:30 - 2:30 - Play
2:30 - 4:00 - Nap
4:00 pm - Wake, eat
4:30 -5:30 - Play
5:30 - 7:00 - Nap
7:00 pm - Wake, eat
7:30 - mellow interaction, bath time, storytime
8:00 - Bedtime
For the first 2 weeks I would put him down at the "scheduled time" and wake him up ... after a couple of weeks he did it on his own and followed the routine. It was great to know when we could leave the house, have dinner with friends, etc.
I wish you the very best. Type out the schedule for your family members and it will all fall into place. If you need any support, please let me know.