I'm not sure I agree a Scandi look needs loads of money to carry off. Minimalism yes but pared back Scandi style not so much. IKEA and H&M home is good for a lot of the components of this look. It's about lots of natural materials and textures. Think about shapes as well, is everything boxy or do you have circles and lines as well? And have lots of wood, preferably vintage.
What kind of house do you have? Is it a new build or mid century or a period property? What kind of budget do you have?
For your sitting room I'd spend ages choosing a good white then paint the walls, ceiling and woodwork in the same matt colour.
Stick a very large paper lantern (lots about, John Lewis and Dunelm do some nice ones) on your central ceiling light (or you could get a spider rose and hook several up, cheap but effective). Depends how high your ceiling is though, if it's not high then a mix of wall lights, floor lamps, table lamps, portable lamps and fairy lights make more sense. You need lots of sources of light to make it feel cozy, aim for 5 or 7. For interest mix up styles and eras but keep to your neutral colour palette.
Cover the ugly laminate floor with the biggest rug from IKEA that is made from a natural material, something like the jute Lohals. Or you could layer natural rugs with the IKEA black and white Stockholm rug, depends how much texture you can cope with.
What kind of sofa do you have? Something like the boxy Swyft no3 would fit. Or go for something with a MCM asthetic or even a vintage sofa that you could get reupholstered. A leather sofa might work as well as long as you go for a natural brown colour. Depends how much room you have. Then some accent chairs with lots of wooden legs and arms on show and lots of vintage MCM options on vinterior or ebay. Do not have sofas backed against the wall unless the room is very small. Have cushions in a mix of textures but in a tight colour palette and preferably natural materials. No matching. And nice blankets in cotton and wool.
Think about TV location, try and avoid having it the opposite corner from your door. Then think about what else you want, e.g. do you need a desk or bookshelves in this room? If you need lots of storage get IKEA storage or go upmarket and get Vitsœ.
Art work go big, there's lots of abstract art on ebay that can be picked up cheapily that will add impact but not detract from your asthetic (lots of shite as well but it'll be worth trailing through to get what you want). Or go for a gallery wall of family photos or kids art or magazine covers or whatever is meaningful to you. But think about what else is going on and if too much visual clutter will stress you, I have very little art in my sitting room because I have so many bookshelves in there. So my art is elsewhere.
So basically texture, wood, light and vintage.