I am always looking for fun learning activities that a one year old and a three year old can both participate in together. Music time has become one of our favorite shared activities. I have devoted one of the drawers in my daughter's room to music, which has worked out perfect for the smaller instruments. When we are ready for music time, I just pull out the drawer, gather up the bigger instruments that don't fit in the drawer and then set it all out on the ground. I let the kids pick whatever instrument they want. Sometimes I play music in the background, sometimes I put play fun children's songs from YouTube, and sometimes the kids just go crazy making their own band.
Musical instruments can get expensive, so I stuck with basic rhythm toys and toddler safe instruments. Every month or so I try to add something new that still fits in the drawer. I found most of the smaller instruments at my local school supply store.