Print area size
print method: FDM (plastic filament) and SLA (photo-reactive resin) are two of the most common
layer resolution capabilities of the printer
budget
single or double extrusion head (FDM)
ease of maintenance
customer support availability from the manufacturer
what type of material you want to print in (ABS plastic is very popular/common and cheap-ish),
Also something to consider: what kind of 3D modeling software is best suited for your needs. Programs like autocad and solidworks are great for precise engineering but are tougher to use to make organic shapes or animation type characters.