Hi,
I don't recommend to allow customers to be able to checkout with both "to quote" products and "to pay" products at the same time, that will be too confusing and will require quite a bit of customization of the views.
Instead, I'd recommend to have two warehouses configured, with the products of both types in their respective warehouse.
And then have your shipping methods for the "to pay" products by restricting them to that warehouse and then another shipping method for the other warehouse.
And then have your normal payment methods restricted to your "to pay" products shipping methods, and a "collect on delivery" payment method, renamed "request a quote", or something like that, restricted to the "to quote" shipping method.
That way, on the checkout, people will be able to pay for the products of one warehouse or request a quote for the products of the other warehouse.
And if they have products of both types on the checkout, they'll get an error message and won't be able to finish the checkout.