Nice looking place, Kathlee! Here are my suggestions: add tiered plants on either side of the stoop, coat the landing with colored stucco or paint it, and hang an interesting light above (if there isn't one already).
Anything that says, 'Welcome! Come on in!' always works well.
Best of luck to you in your new home!

Talk about a blank slate! It's so hard to say since the picture is only of the stoop. I would like to see the entire front of the house. First you need to figure out how much sun the site gets. Are you going to do foundation plantings in the dirt on the side or are we strictly speaking of container plantings? Personally, I would consider vines to go up the newell posts, Mandevillas are nice if you want an annual in a pot. Put a few more pots of annuals around in coordinating colors and you're set for this summer. And while you're enjoying that this year, plan for a more permanent (read: perennials) entry next year. I second the idea of painting the stoop. How about sunny yellow diamonds on an unpainted background? Have fun!

I'd fix some window boxes on those railings asap!

Kathlee, I'm sure you have a lot of other things to spend money on, so here are my thoughts: Knock off the left hand rail to open up the passageway. It will incorporate the stoop into the concrete pad to the left. Nestle a gardening container in the corner with some tall grass and a pop of color and a friendly welcome mat.

You can find a substantial, high rectangular planter (roughly the depth and height of the stoop) to saddle up to the left side of the stair and fill it with color. I wouldn't put anything on the handrails. That would make them too cutesy. Also consider removing BOTH rails altogether (good suggestion from Alyse), removing the broken stones/concrete from the right side to better define the edge, and taking off the storm door altogether. The screened/storm door is unnecessary if the other windows on that facade open (which it looks like they do). It will also show off the front door more, which you can paint in a bold, eye catching color. Of note, most towns have code about when handrails are necessary, but it is usually dependent upon number of steps. Where I live, it's 3 or more. You might be fine without them. If you need one, keep only the right side.

I agree with Alyse on the knocking out the rail to open it up a bit! Are you in an area where you can put furniture outside without it getting taken? It'd be charming to put a bright parlor chair out front with a reading table, rug, (bring the inside out!) and a lemon tree for the summer months. If not, never underestimate the power of a brightly colored door, a pretty hanging light, or displaying some outdoor art!

The best thing to do (provided you own the property and can make changes to it) is to save your money until you can do a re-design. In the meantime, I'd add some flowers, perhaps planted in a window box on the right-hand side, on the outside of the handrail (so there's no hindrance with entering). To "balance" the look, a large planter on the left-hand side, at the bottom of the stairs would be nice. Stay away from trying to be too symmetrical. This is a cramped space and trying to keep things too much the same on both sides would only call attention to that.

Flowers pots would be the fastest and easiest way. Buy several in different sizes and also add some tea light holder, a water jug or something else to create interest.

Personally, I think I would simply cover them with wood. It shouldn't be difficult, I think.

I guess it all depends on what look you want.

There is not much room for clearance so I would paint/stain the concrete a darker color, put out a nice outdoor mat and fix up the area around it with large potted evergreens. ~Tracy

Like Alyse, my first thought was get rid of that left hand rail to open up your stoop to the lower patio below. I'd get some additional concrete (or wood) steps to connect the two areas. Container garden the heck out of the lower patio, with tall plants or a plant stand on either side of the new stairs. Add a little chair or bistro set and a small outdoor rug. Hang some plants above the stoop itself if possible (can't see the roof line). Paint the trim on your storm door and the remaining handrail a color that pops against all that white.

Eventually paint or tile-over the concrete. Better yet, tear it out and replace with a wood stoop and deck. But for now, this is a cheap solution that will really improve the curb appeal.

Exactly what everyone else has said -- either planters with bright, colorful flowers or flower boxes on the railing with bright, colorful flowers. And a nice doormat.

Do not knock out the handrail without first seeing if your town has ordinance or code requirements about stairs and handrails. Assuming they do not, then you can remove the left railing. I would also suggest that you replace the broken rocks on the right with either concrete or some substantial pavers, to add a bit of symmetry.

I like @typwc's ideas of trellising plants up the rails, but my family recently tore out mandevilla from our trellises because they made such a huge mess that stained the concrete as the flowers rotted on our concrete/tile patio. So, I would just think about what flowering plants to use carefully in terms of maintenance before committing to anything.

I like everyone's idea about potentially taking out one of the handrails to extend the patio out, and in the meantime, plants, perhaps a light, and a door mat will make a big difference.

I had a similar stoop outside the front door of my previous home. I suggest planting rose bushes in minimum 24" diameter pots and placing them on the ground to either side of the stoop. The roses should grow up to about the height of the railings and if you get everblooming types (Floribunda and Grandiflora), you will have cascades of beautiful, fragrant flowers to greet you whenever you enter or leave your home.

First, a doormat.
After that, I'd put some flowers climbing those railings. I'm guessing that the stones to the right in your pic are there for necessary drainage purposes, and in that case, I'd put a pot on the step in front of each railing and start some clematis climbing up each side.

Astroturf!

Don't hit me.

This photograph seems telling as to how you are thinking about this problem. You want your house to feel cohesive, complete, and inviting. How does this entry interact with the rest of the house?

Plants are a great place to start and I could see planters to both sides of the stairs and repeated elsewhere. More neatly placed stones or pavers along the edge of the house might give some detail. Add color to the inner door? Do you have shutters? Are there plants you like elsewhere in the yard? I wouldn't, however, remove one of the railings. I'm not sure what codes are regarding that, but it just seems inherently dangerous - far too easy to accidentally walk off the edge.

since i suck at maintaining flowers of any kind... if it were mine, and doable, i would stencil in some kind of cool design, in a bright (but complementary) color, that meanders down those steps. sort of like a welcome mat, but much more personal!

Stone pavers to cover the cement and hang some plants! Love the railing!

A few potted plants and paint some cat /dog footprints up the stairs and to the door or a welcome mat. Geraniums will probably work well. A larger planting in the open space by the rail would draw attention away from how small the space is.

Matching potted trees on either side of the door (outside the railing) would look pretty and draw the eye out from the cramped stoop.

Eventually you might like to build a proper porch to create a better transition space between the indoors and the outdoors, but trees would help in the short term.