Are you keeping your cabinets, backsplash etc?

It will be helpful to know so we can make recommendations.

Do you have a budget in mind? What are your priorities? For starters, I would remove the curtains. You will still have the blinds for privacy.

Cluttered fridges always jump out at me. I know magnets and pictures can be a source of family amusement but if it is just a mess of random things on there, I would clear it off and clear off the top.

Indoor outdoor rugs work well in a kitchen. You can put a runner in front of your sink or get a larger rug to fill the space.

I would remove the scalloped edges around the window & remove the curtain. If you can remove the scallop in the opening to the other room that would help also. I now see that the top cabinets have a scallop also - if you are able to perhaps remove/sand that down to a straight edge. You may want to remove the doors from the top cabinets and use that for display/neatly arranged storage. It would open up the kitchen some. Yes, remove the wallpaper. I can't tell what the floor is from your pics - you may be able to paint the floor. My best friend painted a vinyl floor and it looked great!

What is next to the stove - is that a washing machine? Is there another place for it? It looks like it is in the way of that hallway that enters the kitchen.

while it's hard to give suggestions not knowing exactly what bothers you the most, budget, etc-I'm with Sylvia here..I'd selebrate the warm vintage-y feel of the cabinets..I might even choose more prominent hardware to make it even more distinct-but that's very personal preference of course. Do the appliances work well or better are to be changed? I'd leave the cabinets be in their heartwarming glory..unless they're in a bad shape or you don't feel towards them anything tender at all, and concentrate on counters, backsplash, appliances, maybe sink..whatever is in the worst shape or bothers you the most. I like the suggestion of soapstone, you have several directions to take it of course, but I'd make it not busy- being it soapstone that does exude a very warm feel, Quartz, Formica, Corian, ,etc

I might have fun with the backsplash though-if you love colors and/or patterns, these will work well. As will simple tile too. Think of the overall vibe you want your rooms to have.

I imagine having counterspace next to the stove would help with the functionality. I did grow up with a stove with nothing next to it, so of course not the end of the world, but would make one's life easier. You seem to have a washer there though..no other space it can go? can it be moved a tad, so you can put someting narrow in between, that'd give you just a bit of surface to put a pot on if needed? not necessarily a full cabinet..I know IKEA carries some units..check them out..smth like this one maybe?

http://www.ikea.com/us/en/catalog/products/00323024/

they have several, different dimensions and materials

Of course if what you're looking into is bigger remodel -this thread belongs then in Kitchens forum(you can copy pase it or add a tag), with you attaching even a rough plan and a list of your main kitchen needs..you'll get major help there regarding possible layout changes and all.

It's a very cute space, congratulations on your new home!