A soft six-panel cap has an easy, off-duty feel. I like it with jeans, shorts and a relaxed jacket, brim pulled low and hands in pockets. The shape works best when it feels broken in rather than stiff, with simple embroidery that blends into the fabric or adds a point of contrast. A baseball cap or bucket hat can bring that casual note to a fall outfit.

On a curved brim, small lettering becomes the detail. Tonal thread keeps the cap quiet, while a brighter or contrasting stitch turns the crown into a focal point. I like a clean six-panel shape that lets the embroidery sit neatly on the front.

For the washed-cotton end of the trend, I would start with Ganni's washed cotton cap in faded burgundy, a six-panel with tonal embroidery that reads quiet from across a room. Faherty's pigment dyed hat in gray has a tiny embroidered sunrise, and rag & bone's white Harlow has a deep brim. For navy, there is Lacoste in plain twill and PARKE in a washed navy with a script graphic. ANINE BING's Jeremy in black has small embroidered lettering.

My tip for any of them: hold the brim up to the light and look at the stitching, then bend it. A good washed cap should look broken in without looking tired.

Caps in suede and smooth leather have an easy argument in a cold October: they look like outerwear for your head. The six-panel shape stays the same, the surface changes, and a plain cap suddenly looks deliberate.

COS has a chocolate suede six-panel with a pared-back finish, which is the one I would take if the point is shape and texture. Brunello Cucinelli's version is refined suede in light gray, a thin leather with a soft, velvety hand. Eugenia Kim's Lo cap is lamb-suede in khaki with a small side plaque. For black, Saint + Sofia's Avalon is smooth leather with a popper at the center back, and Manière De Voir makes a structured brown cap in vegan leather.

Two of these are faux, and that is worth knowing before you buy. 8 Other Reasons uses polyester faux suede in dark brown, and Stand Studio's Cia is paneled faux leather in a powder purple that suits a gray coat well.

Across these styles, the clean six-panel crown is the common thread. Check whether the panels meet neatly at the top button, and whether the surface is even, because suede and leather show every uneven seam. Wear one with a wool coat and straight jeans, and keep the rest of the outfit matte.

What I would skip: a suede cap on a day that looks like rain. Suede marks easily, so the faux options are the safer call for weather.

Embroidery is where this look lives or dies. The test is simple: stitching should lie flat and sit square on the crown, and the thread should be close to the color of the cap or deliberately far from it.

For the quiet end, Polo Ralph Lauren has a green cotton chino cap with a small red pony, and ANINE BING's Jeremy Collegiate comes in deep emerald with a small crest. FRAME's Ritz cap is beige with cursive lettering and a buckle strap, in a restrained palette. Ruslan Baginskiy hand-embroiders a small motif on a brown six-panel, so the detail is tiny and the cap is the point.

If you want words, Sporty & Rich does navy with white script, Treasure & Bond has cream twill with red script, and Varley's Melvin Club is a dark brown cap with a cream script monogram. Clare V.'s Excusez Moi is the loudest of the bunch, khaki with bold neon lettering.

I would wear the tonal ones with a trench or a gray sweatshirt, and the slogan caps with a plain white tee, so the cap is the only thing talking. Run a finger over the back of the embroidery: loose threads or puckering around the letters usually means the front panel will not stay smooth.

What I would skip: lettering that is longer than the panel. When words curve around the seam, they can look more like a patch than a clean embroidered detail.

By mid-October a cotton cap starts to feel thin, and wool is the answer. The surface is fuzzier, the color deeper, and the crown holds its shape in a way washed cotton never will.

Clare V. has a black and white herringbone in a cashmere and wool blend with embroidered detail. rag & bone's Harlow comes in plaid wool, with a buckle tab at the back. A burgundy patchwork plaid cap from a department store house label is in heavyweight wool-enriched fabric, and it is the loudest of the group. Sporty & Rich offers an off-white wool cap with navy brim and serif lettering, and AllSaints uses a wool-blend felt crown with a leather brim in gray. Siegelman Stable makes a chocolate brown dad cap in wool blend with tonal embroidery, and Ruslan Baginskiy joins a wool blend crown to a faux leather brim. Eugenia Kim's windowpane tweed in black and beige has a curved brim and a crisp structure.

A baseball cap can also help protect your skin from the sun, and in wool you get the opposite benefit as well: warmth. What I would check is the inside. A sweatband that scratches your forehead will end the relationship by the second wear, so feel it with the back of your hand.

What I would skip: a thick plaid with a thick scarf. Pick one pattern and let the other pieces stay plain.

Corduroy is the quietest way to get texture on a cap, and it comes in colors that suit fall: olive, brown, navy and burgundy. The ridges catch light, so the fabric adds interest even to a simple design.

Weekend Max Mara's Wkaragno is a wide-wale corduroy in deep brown. ANINE BING's Jeremy comes in fig, a burgundy with tonal embroidery, and Brixton's Big B is olive with a fuzzy letter appliqué. Clare V. does dark navy corduroy with red lettering, and Hat Attack makes a plain taupe corduroy cap with a straightforward finish. Polo Ralph Lauren's sport cap is stretch corduroy in golden brown with an adjustable leather backstrap, Lacoste's is olive-brown with a small croc, and rag & bone's Harlow is a ribbed burgundy cap with rich texture.

When you try one, look at the direction of the ribs. On a good cap they run in line with each panel, so the seams disappear. If the ribs run every which way, the cap will look patched together.

I would wear the olive and fig ones with a camel coat and dark denim, and the taupe with a black turtleneck. The ribbed rag & bone is a lovely option for texture.

What I would skip: corduroy in a heavy rain. The nap flattens and dries unevenly, so keep it for dry days.

I would start with the washed cotton caps and pick the color first. Navy, black or a sand beige gives a relaxed look, and green is worth a look too.

Then I would check three things in order: six panels meeting cleanly at the button, a brim with a gentle curve, and embroidery that lies flat. Measure your head before you order; knowing your size is key.

After that, think about the season. Suede and wool for now, corduroy for next month, cotton again in spring. Choose a cap with lettering or a small motif you actually like. If you want to keep browsing, I also put together Burberry Hat for Women and a slim-buckle belt edit.

If you love the Celine baseball cap, I would give these pieces a look too.