How much money do you have? If you can manage to buy a few toolsheds, that's the easier way to level up pretty quickly.
Queen & Pastrychef, I'm in a little bit of a different situation than you two because I already had an existing farm and just restarted playing. I was already at level 29 I think when I restarted and already had all the cocounut and other trees and animals (I think I had to buy 5 sheep) in storage so didn't really have to buy new ones. I also had about $100,000 from when I had closed the farm, not much but I was able to spend that on toolsheds instead of trees and animals.
But i learned that, if I asked my good neighbours for parts that they would send them to me Some still sent dog bowls, which I didn't mind since I always seemed to need that cash too. It all balanced out in the end and I was able to continue to complete the other goals while building the toolsheds. I also had already mastered strawberries and didn't want to spend valuable space planting those when I could be mastering a tree or other crop or harvesting well needed money from cows or some other such thing.
If you can collect the parts before you buy the toolshed, which I think is what you are doing, then you won't have valuable space wasted which could be used to plant out strawberries.