Cold Weather Gear

Personally don't think brand names make much difference. Where do you live? We use pretty much standard layer gear that we get at Costco and local outdoor stores. Some folks push smartwool for socks but I have not found much difference over the years as long as it is Merino wool. Any silk or synthetic long underwear works. I prefer silk but for your purposes synthetic blend is just as good. Gets gloves with good insulation but not overly tight. I prefer the two glove system.

Look for end-of-season sales at sporting goods stores. Or charity thrift stores (I'm partial to the ones run by American Cancer Society.) Costco has great merino wool socks and 32 Degree Warm shirts/leggings.

We live in Texas where it rarely gets cold. No wool for us.

Windchill here midday in the Heartland is -1℉ so we're thinking about warmth. Lightweight and non-bulky (space-saving) performance underwear is preferred: REI, Patagonia, even Lands End - silk or polypropylene. Seirus gloves, but not bulky ski-gloves. I use glove liners by themselves for most of the time.

For just walking around in urban areas, name brands base layers are not life critical. "Expert advice" from REI should be your reading starting point:

https://www.rei.com/learn/expert-advice/underwear.html
https://www.rei.com/learn/expert-advice/layering-basics.html

For outdoor comfort, your base layer should be made of merino wool
(popularized by brands such as SmartWool, Ibex and Icebreaker),
synthetic fabrics (polyesters such as Polartec Power Dry® or Patagonia
Capilene®) or, for less-active uses, silk. Rather than absorbing
moisture, these fabrics transport (or "wick") perspiration away from
your skin, dispersing it on the outer surface where it can evaporate.
The result: You stay drier even when you sweat, and your shirt dries
faster afterwards.

If you are active in cold weather environments, you would be looking for both moisture transport away from your skin in addition to thermal insulation and wind protection, quality base garments will last a long time and are worth the price. My prefered base layer brands are Craft and Patagonia.
https://shop.craftsports.us/baselayer-guide

I started out with lightweight silk long johns (Winter Silk sells online), which may be the lightest fiber to pack. That matters to me, but it's my impression that silk doesn't wear quite as well as polypro; it's definitely more expensive most of the time. A fellow figure-skating fan (rinks can be cold) suggested polypropylene. I've now switched to Cuddl Duds, but as others said, the brand probably doesn't matter.

One thing to be careful about with silk is that, since it's an expensive fiber, sizes of silk garments can be quite snug. When my silk gear gave way, it was because it split at the seams and started developing runs. In addition, I think it is recommended that silk be hand-washed, whereas I toss my Cuddl Duds in a lingerie bag and wash them by machine (when I'm at home).

Living in Colorado and skiing we each own several pair of Long underwear. My favorite for price, warmth and comfort are the REI brand. If you are going next winter you should watch for sales near the end of this season.

“No wool for us.”
SmartWool, if you aren’t familiar with it, is lightweight and washes well. Another good brand of lighter-weight wool is Vermont-made Darn Tough.

Gloves - I wear REI or LL Bean.

If you think you'll be cold in Amsterdam in early December (or Basel too) and want long underwear, go to any Walmart or Target and buy them. I only wear them when skiing and snow shoeing. Brand names are irrelevant as no one will see the label you'll be wearing. :-)

I also don't pay attention to brand names of gloves. If you prefer access to your smartphone while wearing gloves, make sure the gloves you buy have touchscreen functionality. If your hands get cold easily, also make sure that your gloves are wool or cashmere lined. For temps in the 30s - 40s, I wear 3 button-length black leather touchscreen gloves with a cashmere lining. I got them at LL Bean for $59.

The first two weeks in December can have a wide range of temperatures and precipitation. We have had snow but rain might be more common. A rainy 35-40 is almost tougher to dress for.

We have a REI in town and I wear the lightest weight store brand long underwear. It packs as light as silk and lasts much longer. It also dries out easily if you want to hand wash it.

I usually walk with my hands in my pocket and just use light weight gloves that I bought at a Christmas Market years ago.

A light shell jacket (water and wind resistant) with a hood is maybe most critical. I have a Columbia jacket from Burlington Coat Factory. The REI jackets are overkill. Cheap umbrellas are available in Germany in case you have an unusually wet visit. Couple the jacket with any long sleeve shirt will handle most conditions in December. The long underwear helps at night.

A baseball cap keeps the head dry and the hood out of my face.

A wool or fleece "beanie" style cap that covers ears, gloves and warm socks go a long way to staying warm if you are protected by wind chill. For walking around town even cheap knit gloves or glove liners work if your jacket has hand warming sized pockets that keep them dry.

My winter walking around town socks are medium weight wool or synthetic socks (no cotton) combined with foot wear that stays dry. Don't try to squeeze feet with extra thick socks into a shoe/boot sized for lighter weight socks. The too thick socks will constrict your foot's blood flow.

Bottom line is protect extremities from moisture and wind.

Most people don't need special clothes for Amsterdam or Basel, mid-30s°F to low 40s°F in December.

As a woman,I have one pair of Cuddleduds, but I find that leggings or a pair of tights work just as well and fit better. I saw a great selection at Target this afternoon. My husband and our kids love their lined pants from Eddie Bauer. For temps around freezing, I tend to use the cheap, lightweight knit gloves from Target.

...don't need special clothes for Amsterdam or Basel....

"Special" depends on your normal living conditions. If you live in the southern most state (Hawaii), normal clothing may be shorts and an Aloha shirt. OP's from Texas and while the northern part can be cold with occasional snow. OP may be a Gulf Coast Texan. What is normal winter clothing for Minneapolis may be special clothing for a Bay Cities dweller.