Alstroemeria grow from crowns with big fat roots (think asparagus roots). They grow like wildfire so will outgrow a pot in a matter of minutes.
Around here, in the spring, the stores are full of pots of blooming alstroemeria at reasonable prices. I would wait for the pots to show up at the grocery. There are sizes from about 8 - 12 inches up to 3 or 4 ft.
Here are 2 patches in my yard: