Generic Placeholder Product with Dynamic Pricing

Hello all. Am creating an online tool for people to custom design an art item. They can put in the exact dimensions they require (X" x Y"), the number of colours to use, position/layout of those colours, add-on images, text and more. Then based on that, generate the cost of the item. Am not sure that the Variant or Infinite Options plugins is going to handle all of the complexity of dynamic designing.
My original idea was that the online tool would design the item and determine the cost, then call the PayPal API to process the payment. But am now thinking Shopify may be the better solution - integrated shipping, a POS solution for in-person sales, and can still put up all my other non-customized items as normal store items.
Would there be a way to have a “Custom Artwork” item in my store, that doesn’t have a fixed price, that my online tool could then send the customer to? It would need to accept the price that I would send, along with the dimensions and weight to calculate the shipping. Ideally, it would also accept an image of the customer’s finished artwork to display.
Is this possible in the store with or without some plugin? Or would I be calling the Shopify API and have it add the item dynamically to my store? Or some other process?
Thoughts appreciated!