A scarf is the cheapest way to change an outfit and the easiest thing to buy badly. Almost all of it comes down to two decisions that people make by accident: what the scarf is made of, and how big it is. Get those right and a $210 scarf does more for you than most jackets.

On fabric, silk twill is the one to understand. It has a slight diagonal weave that gives it body, so a twill square holds a knot at the neck instead of sliding out of it, which is why every heritage scarf you can picture is twill rather than a flat silk. A silk satin will drape and slip. Cashmere is for warmth and the number that matters is weight, since a light two ply is a scarf and a heavy brushed one is basically a wearable blanket. Wool and mohair sit between them, and mohair is where you get loft without the price of cashmere.

On size, 90cm square is the classic and the most versatile thing here, small enough to tie at the neck and large enough to wear over the shoulders. A 70cm square is a neck scarf only. A long stole from around 180cm is what you want over a coat, and anything past 200cm is a wrap. The narrow bandeau shapes are a different item, meant for a bag handle or a ponytail.

Forty scarves below from Net-A-Porter, from $160 to about $2,520.

Below, starting with the house with the widest range.

Gucci is the easiest place to see the whole category in one label. The Heritage animal print silk twill is $250 and the best introduction to a printed twill square I can point you at. The fringed logo jacquard and the metallic cashmere blend jacquard are the warm ones, the Floral Print silk twill and the sequin embellished floral are the decorative ones, and the diamond shaped floral print is the odd one I like most, because the shape does the work for you. The reversible fringed jacquard knit cashmere wrap at $2,520 is the top of the range and functions as a layer rather than an accessory. Roughly $250 to $2,520.

This is the grid to buy from if you own no scarves. Dolce & Gabbana's floral print silk twill is $235, Valentino Garavani's printed bandeau is $320 and Alexander McQueen's printed silk is $390, so the entry point here is genuinely reasonable. Toteme's Collector logo print is the graphic minimal option, Tory Burch's The Pool is the most fun print in the issue, and Gucci appears twice because the Flora and the printed metallic are two different arguments. Chloé's lace trimmed silk scarf is the softest. Learn one knot, ideally the simple bias fold at the neck, and all eight of these work.

Warmth, and the grid where price and quality track most closely. Loro Piana's cashmere scarf at $930 is the one I would buy if I were buying once, and The Row's Mantia at $1,900 is the same argument taken further. Balenciaga's fringed two tone at $550 is the value pick and its printed wool and cashmere logo scarf is the loud one. Burberry's checked cashmere is the heritage choice, Brunello Cucinelli's sequined cashmere and silk is the dressed up one, Loewe's fringed intarsia is the graphic option, and Saint Laurent's modal and cashmere twill is the lightest. Check the ply before you judge the price.

The practical end, and where the best value in this issue sits. Rôhe's wool blend scarf is $210 and Acne Studios's Canada narrow fringed wool is $220, and both will outlast far more expensive things. The Row's Uma in mohair and wool blend and Jil Sander's fringed mohair are the lofty ones, Burberry's checked wool is the classic, Etro's fringed check and Dries Van Noten's intarsia knit are the pattern picks, and Saint Laurent's Grand Carre animal print is the largest. A wool blanket scarf over a coat is the one styling move that reliably makes a plain coat look considered.

Eight more from $160, including the narrow bandeaux and a couple of hooded and pointed shapes if you want something less conventional. If you are buying one thing from this issue, make it a 90cm printed silk twill square, because it works at the neck, on a bag, in your hair and over your shoulders. Everything links through to Net-A-Porter.

Care is short here. Hand wash silk in cool water with a drop of mild detergent, roll it in a towel, and iron it damp on the reverse at a low heat, which brings the twill back better than dry cleaning does. Cashmere and wool get the same treatment as a sweater, washed cool and dried flat, and stored folded with cedar rather than hung, because a hanger leaves a permanent line down the middle of a stole.

One styling note I keep coming back to. A scarf reads best when it is the only pattern you are wearing, and it reads worst when it is competing with a printed shirt. If you are unsure, put the print at the neck and keep everything below it plain. That is most of what there is to it.

Phoebe