Steam out what you can from the dents before sanding. You can do this by putting a hot iron over a wet rag or paper towel (blue Scott towels are my choice for this), or you can use an actual steamer (I prefer to use an X-Steam Travel Steamer for this on solid wood), which is a bit simpler. For deeper dents, you can try cutting into the wood with a razor blade (ideally in the grain lines) first to open up more fibers.
You can steam the drawer fronts, too. Just don't go crazy with it. If water is running and pooling, you're giving it too much moisture. The heat from the steam should dry the spot fairly quickly. Then sand carefully.
Use Teak for the legs, of course.
Depending on the color you want, I tend to suggest Old Masters 'Cedar' wiping stain when it comes to matching different pieces of Teak. It will give you that aged, red color and is easy to control.
Thanks for the detailed response! I'll give steaming a go tomorrow. Started this afternoon with a good murphy's oil scrub-down. Looks like this one collected quite a bit of grime. Starting to revive that warm teak color.
Anyone have suggestions for where I could source 1-3/8" teak dowels? These legs look very straightforward. I found one place online, but it priced around $200 for the amount I need (5ft). Perhaps that is average? I've never shopped for new teak before...
Teak is expensive, yeah. But you can surely find a woodworker who can make them for you. As for sourcing it, there are small lots that can be had cheaply on eBay. This looks pretty much like what you need:
https://www.ebay.com/itm/Teak-Burmese-2-x-2-x-6-Single-Piece/26350174110...
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