We recently moved in and just started to furnish it. The few pieces we've bought already are neutral. For example, our kitchen table is dark brown, we have a jute rug in tv room with a brown leather couch. We would like to add pops of color with accent pieces and artwork but tend to go for neutral for larger pieces. The room is about 13' x 14'. Down the road, we'd like to put a built-in bookshelf with fireplace on the far wall but for now, we plan to keep the layout as is. Thanks for your help!

Maybe take a look at Ben Soleimeni rugs? https://bensoleimani.com/ Depending on the size you need, some will come in under your budget while delivering a fair bit of neutral sophistication. (You may remember his name from the work he did with Restoration Hardware) I am also a big fan of the Karastan non wools,like the Euphoria line. Hard to rec without knowing more about your style and how neutral you want to be. For example,is this sort of rug too colorful? https://www.rugstudio.com/karastan-spice-market-mossbrae-vanilla---sapphire-area-rug.aspx Too lively? https://www.rugstudio.com/loloi-ehren-ehr-04-oatmeal---ivory-area-rug.aspx#206569x7__73900

Maybe something like this? Abstract/modern design, muted color combination of ivory, cream, and blues?
http://www.dynamicrugs.com/collections/machine-made/mood#3195

Do you like a traditional vibe like this one? The colors would look beautiful in your space. Before you choose a rug I would make sure your furniture is laid out correctly. If you could provide photos of the room from standing in the dining room into the room that captures a view facing your sofa and catches both walls to each side of it we can better guide you.

Would you mind sharing where you purchased your various furniture pieces and if you're happy with them? I really like the look you're pulling together, and I'm having an awful time finding things I like locally (near Salt Lake City). Thanks!

I think your room layout needs modifications. Put sofa on far wall. Coffee table in front of sofa and your pretty chairs angled to sofa. Art over sofa with some blue from the chair color. A rug that is neutral with some blue would be nice. When possible add small end tables and beautiful lamps. I will post some inspirational photos in a little bit.

Something like these

This is a perfect example of how to arrange your room. If possible, i would change out your coffee table. It is rather farmhouse looking and your sofa and chairs are more sophisticated and modern. Plus it is too big for the space.

Before you choose a rug, you need to get the floor plan correct. In order to help with that, could you please provide more information?

1) What is the purpose of the space?

2) Is there a tv?

3) A photo of each wall of the room.

Thanks.

I'm going out on a limb and say that this layout is not the best for this room. This walkway makes no sense.

A layout like this one below is going to work better for traffic through the room. Your sofa and chair selection are really quite nice, but that coffee table is brutal in design compared to the seating.

You can try out rugs in your room on RugsUSA.com