Hello, I am currently trying to work on a project, however I will not ask for any sort of Coding since I want to implement that myself.

I am working on a project in which I deal with various contracts and I have to keep updating the total price of each contract as I elaborate it.

Therefore I would like to know, thinking in GOF what would be the best strategy to use when "refreshing" my contract prices.

Unless I've misunderstood the question here, the only strategy choice is push vs pull, ie do you recalculate the price every time you update the details, or just update the contract details, then recalc the price only when you want to display it.
I don't think the Gang of Four have much to say on this. IMHO it's generally safer to pull (ie recalc from the details every time a price is displayed) than to push the changes every time a detail is updated. Unless you have a large number of large projects (say > 100 Meg of data) the efficiency isn't going to be an issue either way.
Or did I just answer the wrong question?