There is a huge variety of rugs available to match any budget or setting so your options are wide open. You just need to figure out what features are more important to you, ie material, wearability, pricing. We don't have kids but we have animals and didn't want to invest a lot into a rug that may not wear well. I found a huge variety at of all places, Home Depot. We ultimately got this one for under 400.00 for a 10x12. One of the great things about it is it cleans easy, it's nice to walk on and it's wearing exceptionally well. It's made by Mohawk and is polypropolene. The lighter coloring really brought life to our fairly dark space.

<div><a href='https://www.houzz.com/photos/home-design-ideas-phbr0-bp~/pleasant-living-room-detroit-phvw-vp~102939745' target='_blank'><img src='https://st.hzcdn.com/simgs/6741987209cbc370_8-6071/home-design.jpg' alt='' border=0 width='480' height='640' nopin='nopin' ondragstart='return false;' onselectstart='return false;' oncontextmenu='return false;'/></a></div><div style='color:#444;'><small><a style="text-decoration:none;color:#444;" href="https://www.houzz.com/pro/prmcustombuilders/prm-custom-builders-llc" target="_blank">Photo by PRM Custom Builders, LLC</a> - <a style="text-decoration:none;color:#444;" href="https://www.houzz.com/photos/home-design-ideas-phbr0-bp~" target="_blank">Search home design pictures</a></small></div>

"I tend to lean more traditional/conservative with some pieces such as furniture, but I don’t mind fun splashes of colorful modern artwork that I can switch out when I grow tired of it. I hope that makes sense. I love the pottery barn look." This is what you said, and actually this is the way I encourage my clients to think (unless they have unlimited funds to change out more permanent items every few years. 1) So, hearing this, you should not buy the coral rug, unless you want a coral theme for 15 years. Instead, buy a textured rug (or you can live with or no rug at all (and spend the $ elsewhere). 2) I would choose a piece of modern art for the buffet and go from there 3) You say you like modern art, but I see none, with the exception of Bessie that is more contemporary that actually modern. But, at least not traditional 4) Stay away from too many word signs. I already see 2. That trend has sort of come and gone Just being honest with you. It begins to look like a Hobby Lobby store. 5) The hug clock thing has also come and gone. It also looks very traditional. 6) Overall, you have too many large dominant things on your walls. 7) Start with the dining room and make that fantastic and move from there. 8) Table near the stairs is overloaded and the checkered theme looks like something you should move away from. I would eliminate that table altogether. 9) Once you choose art, I would put something more colorful in the center of the table. 10) If you do want a runner, that can be looked at, but I'd get something that fits the length of the table.......does not run over the ends. Consider something unique. Here are some photos I pulled right off PB. Notice they all have dark tables and neutral rugs with a pop of color. Traditional and modern mixed. Can change the art at any time and have a totally different look. Cannot do that with that coral rug. You are locked for 15 years.

I like the one Susan put in here from overstock but I would either find a similar curtain set and do 2 rods, all the way to behind the archway at the top and those stay open with a second rod for the liner.  For the liner, you may have to sew an extra amount on the bottom from a second liner to meet the length but maybe see if you can find one long enough first.  Inspiration picture below