Hard to select first gear, pulsing drone at speed.

Could be two unrelated issues, and the pulsing drone only really kicks in above 40mph so isn't my biggest problem!

Gen 3, 2009. First gear is getting harder to select though, and sometimes second. Also got a bit of a clonk noise when changing gear that sounds more like it's coming from behind me, eg not in the gearbox itself.

I can move the gearbox a few mm side to side with very little effort under the car around the rear engine mount. Given I think it's easy to change I'll probably do that anyway. But any other things I should look at?

Thanks

I agree that you need a new rear mount everything should be reasonably firm and not able to move about. The pulsing could be because the drive shaft is not running in it's preferred position due to the gearbox mount or it could be something else entirely.

Difficulty to select first gear when standing still is common on a jimny and could be a bad clutch cable and/or play in the gear lever bushings from wear and tear.

clonks in the driveline is also common from play in the diff and transfer case and all. Usually not a big concern with a bit of that.
Best to get under there and check for play in the driveshaft U-joint where play should be none. A bit of play when you turn the shafts around their own axis is ok but, there should be no noticable play when you lift the shafts up-down.
The gear wheels in the gearbox, transfer and diffs must have a bit of clearance between them to do their thing, It could amount up to 10-20 degrees when you turn the shaft by hand under the car.