A couple of points:
1. I am used to using the following general distinction: we rush
for things (nouns) and we rush
to actions (verbs).
The rush for gold, the rush for Arctic oil, the rush for Supreme Court review of health reform, The rush for digital skills, the rush for retail space...
Cambridge (UK) Online Dictionary:
Quote:rush noun ( HURRY )
[S] when you have to hurry or move somewhere quickly
Slow down! What's the rush?
Why is it always such a rush to get ready in the mornings?
Everyone seemed to be in a rush.
He was in a rush to get home.
They were in no rush to sell the house.
•
[S] when a lot of things are happening or a lot of people are trying to do or get something
There's always a rush to get the best seats.
I try to do my shopping before the Christmas rush.
There's been a rush for (= sudden popular demand for) tickets.
•
[S] when something or someone suddenly moves somewhere quickly
There was a rush of air as she opened the door.
They made a rush at him to get his gun.
•
[S] a sudden movement of people to a certain area, usually because of some economic advantage
the California gold rush
•
[C] in American football, an attempt to run forwards carrying the ball, or an attempt to quickly reach and stop a player from the opposing team who is carrying the ball
2. In general, in US English, modernize is spelled with a z, and British English has 'modernise'.
Of course, these things are largely a matter of style. You will find plenty of rushes to nouns and rushes for verbs, and plenty of British spelling of -ise rather than -ize, but I would prefer a rush to modernise or a rush for modernisation.