Hello,
we're setting up a new website for a saw mill. I can't show much yet though because there isn't much to show besides header and footer. I'm pitching you the idea of our goal and hope you can give me hints on the best approach to achieve it.

Basically the key functionality has two components, a product list and something like a cart.
The product list is a simple list of products with fixed values most of the time and the visitor can merely enter the amount that he wants to add to the "cart". But - and that's where I struggle - for some products the visitor should be able to add his own sizes and create an individual "product". This "product" is only visible for him and only exists until he sends the request for quotation in the cart (or deleted it from the cart). And he should be able to add more than one "product" per product list.
The "cart" is merely an overview of selected products and their amount and the functionality to add or remove products. All it does is provide a form for additional information like name etc. and then send an email as a request for quotation to the saw mill.

I think some of the features (like the "cart) could be done in a shop. But this isn't supposed to be a shop. There will be no prices displayed and no SKUs. And the visitor should not create any user accounts or log in to send requests. All he should need to do is to go on the site, select his items and then send the request.
I only have rudimentary experience with Drupal and hope there is a simple solution to this despite the specific nature of the issue. But I think I just need somebody pointing me in the right direction and figure out the rest of it myself.

I made a little sketch for what we are going for on those product lists: Adding a product