Not gotten to the point yet as all our furniture is log furniture, it does no go out of style in a log cabin and it is built heavy duty and lasts. So far we have only replaced coffee tables with Foosball coffee tables and couple or rooms to go coffee/end tables with our custom made ones. What I do tend to replace is area rugs,
throw pillows, bedspreads. Soon i may need to replace leather sofas.
i would also look at cookware and toss especially worn/scratched.
Also look at your lighting - it makes a big impact often not for too much money. maybe update chandeliers and vanity lights to new style, or at lest see if lamp shades need replacing.
I have pine cone themed lighting in on of my cabins that I bought at a discount ff ebay. IMO it gives just a right touch and does not look like big box store standard stuff.
We haven't had to replace our furnishings since buyinig, but I did have to replace things when we bought the units. Although they came furnished, they had the feel of high-end middle age-- the furnishings were super nice, but very true to the age of the units (about 10 years old when I bought).
For about 10K per unit I was able to refresh all the furnishings by replacing key pieces, refinishing some (for example, giving a pine sleigh bed a dark espresso stain) switching out light fixtures, replacing the linen, etc. I find that replacing dates artwork for something quirky or modern makes a big difference, too.
I get some amazing things from Craigslist and FB Marketplace. A guest never knows if you paid retail for your Thomasville bed, or bought it for 10% of retail on CL. And besides, once they scratch it the first time with a suitcase, its only worth 10% of retail, anyway. There is also a hotel liquidator not too far from me, and they often have very nice, commercial quality lighting, etc. I find most bedding and linen at BBB (20% clearance is a pretty good deal); HomeGoods; Dillards clearance; or Restoration Hardware clearance. Obviously, I'm not one to pay full price when I can create something amazing from a clearance rack. ;-)
Hope that helps.