I personally would use anything with any 'cut' in as they call it. If you do the sanding stage properly then it should polish up nicely. Most polishing compounds with cut or abrasive in are designed for metals not woods like willow. You also want to look out for something that seals the wood rather than just makes it look pretty and shiny as it will soon start to absorb or loose moisture depending on where it is, particularly if you don't oil it as part of the process.
Speed wise slow is better. Mines around 1400rpm I think. As long as you don't put too much pressure and allow heat to build up you should be ok.
Tbh if the sanding is done properly you can get the wood to look great by hand polishing. Takes some time but can look good. Preparation is the key with most things