Hello all, Just bought my first Samurai yesterday and I noticed it has a vibration in first and second gear. Once in third its fine. My first thought would be U-joints but unsure if I should do the center shaft or rear shaft first. any advice appreciated.

If you don't know the history of the vehicle, it couldn't hurt to change the rear drive shaft joints.  In fact, if you don't have the recent maintenance history on the Sammy, I'd be making  a punch list of maintenance to be done, prioritze the maintenance tasks and start knocking them out in the prioritized order.  Establish a base line of maintenance performed for your knowledge.

Brakes, u-joints, fuel filter, air filter, oil change, etc.

Inspecting the front suspension components would be on the list too.  Look for loose/worn tie rod ends, ball joints etc.  Worn front end suspension components can cause vibrations at differing speeds.

Ok cool thanks. I have been doing that, just wasn't sure what some of the weak points on these sammis are.