Define “finger joint”, because that means something really specific:
These days finger joints are done using a special router bit on a standard router table like our Incra (which will do this just fine, but you’ll need to purchase the bit (I might have seen an old one in the cabinet the other day, but maybe not), sized correctly for your build,
Comb joints are usually done using various dovetail techniques. They have square alternating tabs that lock together:
Variations of these joints can be done on the CNC Router, but require practice and a trail of cast off’s, because your first few tries will disappoint you. All about managing those inside corners, You can use either Fusion 360 or vCarve Pro to do it. Both will import STL files, subject to various conditions.
I would not build furniture with MDC. It’s really pretty weak material, and will buckle easily if you use it for load bearing or vertical surfaces. It can also be a pain to paint.
You can make some exceedingly fine stuff with el-cheapo home depot dimensioned lumber. Paint it with milk paint, and it’ll last longer than I will. Added benefit, dirt cheap.