Basswood is pretty soft, so be careful with it as it will dent easily without a finish on it to harden up the surface.
Sanding has two purposes. 1) to get the surfaces (especially the top and rear on a Tele) as flat as possible to make a commercial-level finish possible and 2) to remove any tooling marks (mainly on the curves on the sides).
For 1), using double sided tape to stick sandpaper to a flat piece of wood, or a bit of flat metal helps you get the flattest overall results. For 2), its freehand sanding, or sandpaper wrapped or stuck to a tube, but its definitely the hardest of the two processes.
Keep going with one grit until you've got rid of all the marks from the previous grit's sanding. If you're struggling to get rid of any deep marks, you need to do back at least a grade to something coarser.
If staining, you don't want to go too fine with your grits so I'd stop at 180 before staining. US and EU/P grits are the same up to 220/P220, so no need to worry at this stage. After that, the US grits are finer for the given grit value. Comparison chart here.
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