Dresser update help needed,my first DIY

I would love a suggestion as to how to update an old Hrminy House dresser. a couple of spots are missing a bit of veneer . Should I remove a the veneer or use wood paste and sand before painting, This is my first DIY

thanks for any suggestions

it's solid wood with a veneer on top nd horrible knows that have to go.I really don't care for farmhouse design but I'm open to someone with experience in this area . Thank you

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