Hi Adam,
nice bike, the WNG. I don't know much specically about Ariels (I'm a Triumph man, through and through), but may be worth checking the standard stuff, such as;
Ensure no play in girder forks (if there is some play, I know a great guy in Sussex who rebuilds them), ensure wheel bearings are good, check for good cylinder compression, make sure front and rear wheels are in line (to ensure the frame isn't banana shaped), get her up to running temperature then shut her off, and make sure she restarts ok.
Just a few ideas, there are plenty of WW2 iron fans on this forum who know far more than me who may suggest a few more.
Dont forget, it might look good in photos, but still check it through thoroughly, some people are good at disguising horror stories!
Good luck with it, hope shes a nice one