The final version of the Wii internet browser will be available in March, it will continue being free until June. You will be able to continue to use the browser after the price kicks in. Both Nintendo and Opera have said this so unless something changes everyone with a Wii righ now, or who gets one before June will be able to use the final version of Opera for free.
Also, the trial version is not a trial version, it is a beta. That is why you will notice it locks up your system a lot and doesn't have all of the features promised, like full java support...