I'd first look at what I had, and then add a few low cost pieces to integrate my orphans (the pieces that don't get worn because they don't go with anything else. I love fashion, and I always know what's trending, but I don't like spending money and I have no problem wearing 'past season' items if it's something I like that fits in with my look. I'm not buying a whole new wardrobe every season, and I don't fall for the hype re: brands. I'm having good t-shirt scores from Sainsburys recently- nice quality fabric, decent shapes. I don't do 'investment pieces'. I think that's a bit... laughable.
I'd start with basics first: not exciting, but the workhorses of the wardrobe. Long sleeve tees, a vest to wear under the slightly too see through blouse, a fine knit jumper to wear with those trousers that don't get worn because... then a fun, more 'this season' piece, so maybe you could update your look with just the addition of a pair of new shape shoes, a waterproof ballet shoe, a sneakerina, a new pair of trainers, that kind of thing.
If I find a great colour/shape tee, I buy three, because it's likely they won't exist in the same way next year...
Depending on your lifestyle and personal style: no point buying a suede cropped funnel neck jacket if you spend time every day standing at a bus stop and you live in Glasgow. If you live in a city, and drive everywhere, you probably won't need a massive waterproof technical puffa jacket. Those ballet shoes will fall apart quickly if you're walking three miles a day on your rounds. Of course, that's all pretty obvious, but when we're going for a new wardrobe sometimes we forget who we are and what we do!
1 Coat, £100, 1 shoes, £60, 1 bag, £60. These should go together, in terms of 'style'. I would look for more 'classic' style in these items, rather than something massively coded for 'this season', as next year, they'll look dated and you'll want something else. So, a long single breasted woollen overcoat, or a trench coat, won't set the world on fire, but can be worn everywhere, for everything, don't date too quickly, can be coded smart or casual. 2 trousers, £50 each, 1 jean, £50. a shirt/blouse, £50. a lightweight knit, £50, a versatile day dress, £50, a pair of flat but fancy shoes, £40. 5 t-shirts. £20 each, 1 'nice top', £50. All in... £710. Now... if you're willing to trawl about, a bnwt coat on ebay might only cost you £30, look to sales for shoes and a bag, possibly save a few pennies more. Sainburys' t-shirts are £12-16, Matalan jeans in the sale right now, £15, etc, etc. You could probably get this nice little haul for around £350 if you shop around and have the time to do a bit of vinted, etc. Fabric composition is important, so a high cotton content jumper will look better than an acrylic one, and be less spendy than a cashmere one, for instance. Then you can, slowly, start adding things you need as an when. A small haul in winter for a few warmer knits, a sparkly skirt for xmas, a few linen pieces in summer, that kind of thing.
I buy most of my items from ebay! I love ebay. Bought two fabbo dresses this month for winter restaurant visits for a tenner each! Velvet, boho, paisley numbers, last month I bought two linen blazers for a tenner each. I keep a loose list, which I update every season, but I tend not to buy for 'this' season, but the one coming or the one gone. That way, I find discounts, bargains, and I can see where my gaps are or what needs replacing. Most of my 'ordinary' things come from M&S or supermarkets, basic tee shirts, socks, undies, everything else, the magical bay of E.
I too, am a scarf person. I love a scarf! A pair of plain trousers and a simple tee and I can be 'insousciant french lady' with a silk zebra neckerchief, I can be 'global traveller' with a massive ikat shawl, artfully draped, or a 'modern grunge' type with a checkerboard scarf tied around my waist. In the same old basic trousers and t-shirt combo.
This winter, I'm all over knitted woollen triangle scarves... a cheap little update for my winter vibe, matching items I already own and have bought over the last few years. And I've bought a cream version of a quilted jacket I already have in blue and khaki because I love the shape. And a pair of cream jersey slouchy trousers. That's me done. Of course, I eye things up. There's always new things. But... I'm not buying much. I don't need to. I already have tonnes of garms. I drag them out, decide what I'm liking this season, add a few little things here and there, and... ta dah.