As a note, the Malbon sponsorship is the shortest path to the achievement, it has only 2 levels. That said, you are forced to start with the "The Gold Club" sponsor (which has 5 levels), and will likely have most of the first level done when you can pick something else.
It is always better to complete all 3 objectives - don't take a contract where you don't think you can get one of them. If playing on one of the easier difficulties (or for very skilled players), it is also more economical to take an easier level if you can knock out all 3 objectives in a single round.
Playing on easy, I've maxed 3 of the sponsors just past the Royal Championship.
Levels required per sponsor:
Ben Hogan: 6
Royal & Awesome: 4
Tattoo Golf: 6
The Gold Club: 5
Under Armour: 6