Custom E-Commerce for my site

This is the website where I would like to add a e-commerce: http://laurpojad.com/catalog/base-material/

Under Catalog you can understand what products are there.

I would like to add a custom ecommerce on every product page, where are no price, no shipping, you just need to fill some custom fields, then add to cart. In the cart, you can still change those custom fields. You also need to fill out your personal information, then it will send your order as a e-mail to the company.

Purpose of this e-mail is to send a price request/inquiry to the company. Company will send back that order with prices and then the client decides if he/she wants to continue.

Also what should not be forgotten, that all the products are not the same, some products doesn’t have lengths for example, so It wouldn’t show on the product page nor in the shopping cart.

Is there some kind of plugin or ecommerce that just lets me to add id or something to those table cells and when clicked add to cart, it will send filled custom fields with those numbers that client entered to the shopping cart.

Here is a working example: http://www.puumarket.ee/?op=body&id=42&prod=146&sid=4518

So my question is what kind of ecommerce or plugin can give me this solution to my website.

It would be great if these features can be added too: • Send order email look can be customized (html and css), just like contact form email • In the future, if company wants to expand, so can this solution. Like now there are prices, custom shipping method, custom payout method and so on. Basically just like any other popular ecommerce can do (Magneto, WooCommerce etc.)

Here is a more detailed look of my e-commerce idea: http://www.upload.ee/files/4474150/Custom_E-Commerce-2.pdf.html