The room is lovely and bright but imho needs more colour, pattern and texture. Plants (faux are fine and far more realistic these days - we have a couple from Dunelm that are very convincing) would add life to the space too.
I think it needs personality which isn't necessarily achieved by buying everything at once from one place, however tempting it might be to create the full package in one go.
It's far better to buy what you love when you see it - our furniture and decorative stuff such as art has been collected over a number of years and from a wide range of places, such as ebay, carboots, fleamarkets, antique fairs, auction houses and shops such as Homesense/TK Maxx. That way you can spread the cost too which is always a plus!
Regarding a rug - we've always bought them larger than necessary and ensured the front feet of the sofa(s) sit on top. It makes the space appear larger, imho.
The TV stand is very dated, but there are so many options out there you should be able to find something that suits your style, space available and budget. I'm not usually a fan of wall-mounted tvs but in certain circumstances this can be the best decision. Until 18 months ago we had a smallish TV sitting on a huge antique sideboard where it frankly looked a bit silly. We briefly wall-mounted it above the sideboard which was actually an improvement.
Now we have a new, larger TV that would have been way too high for comfortable viewing if placed above that sideboard, so we took the decision to sell the massive sideboard and replace with a lower, mid century one that is just a little wider than the TV itself.
Here's our TV stand and rug (to give idea of size, not colour)....