If you want to buy a player, bid for them about 1 or 2 million above the asking price. This ensures you of signing that player. Players that are worth buying include:

Thierry Henry
Ronaldinho
David Beckham
Ronaldo
Tim Howard
Roberto Carlos
Alexandre Del Piero
David Bellion
Ruud Van Nistelrooy
Hernan Crespo

In the first year, it is almost impossible (unless you bid over 5 million above the asking price) to buy Thiery Henry, David Beckham, Ronaldo, and Del Piero.