This is probably a good point to point out that the standard US and Australian/European sandpaper grit gradings are quite different above 220/. So the 320 that Waz is talking about is P320, which is very close to ANSI 240 grit.
A comparison chart here:
https://www.thesandpaperman.com.au/a...ion-chart.html
The grits that Wudtone talk about on their UK website will be P type grits as well.
Get the scratches out, smooth off and then go back over with the recommended grit if necessary to rough up the wood slightly. Different timbers will take up the stain differently, so some you may be able to use a finer grit on than others. As long as the surfaces are all (relatively) flat and smooth, you'll get the smoothness from the finish coats.