I would typically say furnishings as it is way easier to find a paint color to work with your furniture than to find the perfect rug or couch to go with your walls. However, If you really can't live with the current colors I would probably paint it something neutral before moving in.

furnishings first! Wall color is the last thing you select in a room.

Most experts advise waiting on the paint until you have a chance to see how your furniture looks in the new place's light. In fact, they often list painting before you move in as one of the top mistakes people make. I agree with them except in cases where the wall color is truly unliveable.

Plus it's way easier to paint before you move in!

I would find a neutral that works with furniture/decor that you generally like. If you do like bold pieces then maybe a neutral would be good anyway so the walls aren't competing with your more interesting stuff.

If it's going to take you a while to get furniture, I would paint before moving in. Go with a neutral color paint--you don't want to live with colors you hate.

I'd do furniture first. Easier to find paint colors than nuances of furniture colors.

We are moving from an apartment to a SFH. The paint colors are murky greenish/yellowish and I want something cleaner. The problem is that we don't have much in way of furniture that we will take with us. Most of our stuff is ikea or hand me downs.

I thought I would pick colors first and have the house painted before we move it but wonder if that is a baddies did will be stuck trying to find furniture to played the it. My taste in furniture and decor tend to be colorful- think Indian/Mexican earthy shades and bright colors so they are not easy to source.