Repainting a kitchen is not a quick job, and therefore this isn’t a quick guide either, so make yourself a cup of tea first and get comfy before you read on.
A quick-drying, non-shrinking filler will be adequate for this. Slightly overfill any holes, and when completely dry, sand smooth and level for your base product.
Tape up your walls and/or tiles with the masking tape where they meet the carcass of your kitchen and along the floor if you are unable to remove your kick boards.
For solid wood kitchens, a primer like Zinsser BIN or Zinsser Cover Stain would be ideal to block any oil or tannins that are ingrained in the wood and can bleed through into your paintwork.