So the minimum $250.00 is for Products in Category 1 not for the whole Order being $250.00 ... correct?
You could probably customize the Minimum Order add on to only look at the Products from this Category to verify that these Products are $250.00 or more ...
So the Minimum Order customized to only look at Products in Category 1 manages if checkout is allowed ...
Table Rate table manages what the charges for shipping should be (Free Shipping Products will have their Price removed from the Calculation automatically)
Again, the Free Shipping Products should manage themselves on the shipping ... and unless the Category 1 Products are in the cart, all should be fine ...
So, your tasks are:
1 setup Table Rate table for Category 1 shipping
2 install the FREE SHIPPING freeshipper to manage a cart of only Always Free Shipping Products
3 Install the Minimum Order add on and customize it further for managing just the Category 1 Products when in the cart