As with all fine finishes, preparation is key. You simply cannot achieve a deep shine without the underlying surface being smooth and completely free of surface glue.
You have two tools to select from: a well-tuned scraper or sand paper. If you sand, you need to progressively work your way to 320 grit before the wood is ready to accept your finish. That is, unless you’re planning to stain the wood before applying the top coat, in which case you need to stop at 180 grit. Anything finer than that and the ability of the stain to effectively colour the wood is going to be limited. Then, ensure the stain is fully dry – at least overnight – before applying the top coat of your choice.
My final guidance on sanding is this: when sanding with machinery, regardless of whether you’re staining, always do a final hand-sanding with the grain to ensure there’ll be no sanding swirls to contend with.