Leave the hardwood and just change out the kitchen tile.

Where is this "tile" going? If at the entry, what about running the wood to the door? I see 3 flooring types already which is typically one too many.

The plan is to remove the wood floor in entrance and install new tiles in entrance and in kitchen.

Match the tile at the doorway then or rip them and use the same throughout.

Glossy to me sounds slippery in conjunction with water, so not the best choice for a floor where there may occasionally be water. It looks like what you have now in the kitchen is textured. You can get matte tile that isn't textured.

You have a whole universe of tile and different color grout to go look at. Using a light epoxy or urethane grout would upgrade the look of the kitchen tile you've shown. Larger format tiles in matte with matching grout could look good. Large Format Porcelain Tile - Arizona Tile