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From the YouTube video I was watching last night on sanding solid wood dinner table, 150 to 180 grit depending on what finish you are going for. He was using a belt sander first and then finishing off with orbital. Link below in case it's useful.
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If it was me I would random orbital it clean with P150. Then hand sand with a block at P120 then P180, maybe 240 if I could be arsed.
You’ve got a job there to avoid cross-grain sanding, hence the hand sanding.
Then a good quality Danish oil (e.g Briwax).
Are you sure those panels aren’t veneered? They often are in a frame and panel construction.
Pics would help.
If there's a thick layer of varnish on it now then it will be faster and easier to use paint stripper to clear the bulk of it then sand.
Danish Oil gives a nice matt finish. Otherwise have a look at what sounds appropriate in your DIY store.