Nothing seems to give exp compared to catching pals. You get like, 2 experience points for everything you build / craft which adds up to maybe 100 points when you’re done.
Meanwhile you can get thousands of exp from catching one pal outside your base. It is the only way to level. I think its an interesting mechanic.
Just farm paladium at your nearest lake, make 300 pal balls, then go catch 10 of everything around your base.
After that focus on mega balls and use those to catch the higher level creatures you find as you go exploring. The system is designed to encourage exploration.
UPD: Find and hatch eggs. Super fast exp. And then start breeding. No need to catch 10 of everything. Just one male and one female. Then breed the other 8.