if you stain the wood it will look like a cave.

Remove everything, the clutter is distracting. Can you remove the paneling/wainscotting?

Is the railing wood or metal?

replace the light fixture with something beautiful, paint the walls and ceiling to unify... get a patterned rug.

IMO leave it save up and do all the same flooring everywhere it looks like the sales outlet store right now. Is the front door your style ? Does it suit the house . Many things need to be considered before beginning to add decor .This a new to you house so maybe just take some time to really figure out what you want to do with the whole house , the entry is the introduction to your home so needs to be well thought out . Is this the only entry the family uses? Since you do not have space for a closet you need to be diligent about stuff not left in the entry .

I only see your entrance and not much on the adjoining space so everything I show is very neutral. The wainscotting can be painted white and above can be either painted in a colour to coordinate with adjoining spaces or install a wallpaper. You can install a runner in the stairs, something that stands up to traffic, and install attractive looking coat and key racks.

Remove all clutter. Add a single large piece of art or a big mirror on the left wall perpendicular to the door. On the wall next to the door hinges, add four or five hooks for coats and tote bags.

There is no room and no sunlight to decorate with live plants. Fake plants only look good where they could plausibly grow.