Clunky is normal. Especially when cold, it will have a big 'thunk' when putting it into 1st. Don't try to down shift into 1st while moving as you slow down. It's easier to do damage that way. Wait until you're stopped. If you have difficulty getting it from neutral into 1st, let the clutch out in neutral, then pull the clutch back in and try again.
As others said, fresh oil helps. Yamahas tend to get a little clunky shifting when the oil is dirty. And lubing the pivot points on the shift linkage is a Good Thing™ too.
If you have an older FZ6 with the cable clutch, there will be an aluminum wheel with a retaining spring at the clutch lever to adjust. If the clutch is not fully disengaging when you pull the lever, this could also be part of the problem. You want a little free play in the lever before it starts to have tension, but not too much or you won't get full throw of the lever to disengage the clutch. If the clutch is dragging a little, it will make engaging 1st more difficult and clunky.