For warm winter you just need basic insulation and a windproof coat. A shirt, a sweater, a windproof coat for your core. A skullcap for a hat or something thicker of you'd like. Wear pants, socks, and proper shoes that are a bit water resistant.

Then check to see whether anything is still getting cold. Hands cold even when in your pockets? Get some liner gloves. Legs making you cold? Get some thermal underwear and some windproof pants. Feet getting cold? Get some thick socks, probably wool ones. Core getting cold? You probably need a dedicated fleece or (synthetic) down layer. Head cold? Get a thicker hat. Neck cold? You need a jacket that zips up high and has a hood.

Your core warmth is most important, it'll make the difference between a dangerous situation vs. an uncomfortable one. Consider getting a fleece or (synthetic) down layer as your first upgrade after a windproof coat. Thrift shops will usually have fleece for less than $10.