Data structure for matching attributes?

I need a data structure and data storage solution that is optimal for the following scenario:

Storing: >20M sets of attributes. Each set is of variable length. None are empty.
Matching: An inputted set with all the other stored sets. Comparing and contrasting attributes. Returning the most favorable matched sets.

I don't know where to start.

Assuming there's a partial ordering with respect to fitness, have some O(n):


best = NULL;
while(t=set->next)
    best = better(t, best) ? t : best;