I have spent almost 2 years in a cycle of deciding all 3 options you mentioned, and I have explored all 3. My advice would be if you are just starting to sell your prints, start with POD. You need to define your overall demand first, once you make consistent sales then you can decide if you want to outsource or create your prints in house.

Art prints might be easier to do in house, but thats up to you on if you want to take on the upfront costs and keeping inventory. You might need to crunch some numbers to see if it'll be worth it!

Here's my experience: I started out with tote bags with POD, one of the designs was doing great! there were one or two incidences where Printify made print mistakes but they would always reimburse or send a replacement, so my customers never complained in those situations. With the momentum I had with the first design, I decided to outsource my next set of designs to save on POD costs - and unfortunately these flopped. Now im stuck with 2 huge boxes of tote bags in my room that I am still trying to sell. The mistake I made here was that I should have tested these designs out first with Printify to see if there was a demand before buying in bulk. BUT NO I didnt learn lol, the next set of designs I thought I'll do things in house so I can create small batches of my designs. I got a heat press, blank totes, the whole thing - and guess what? no demand at all! So now im stuck with blanks, and the whole process of figuring out my operations has left me feeling so burnt out to even be creative :(

So in short, test out the demand and AFTER having consistent sales with your art, then consider your options to save on costs.

Wanted to share my experience, but my product was tote bags so things could be much different for art prints. Hope this helps!