Layering is the way to go.
Most of the modern layering methods work like this: a base layer for wicking away moisture from the skin, an insulation layer to provide warmth by trapping air, and a shell layer to protect against wind/rain/snow.
There are several “systems” out there, but that’s the basics of it. For the base layers and insulation layers, wool, polyester and polypropylene will be ideal. For the shell layer, nylon is great especially with a water repelling treatment. If you’re just in a garage and not exposed to wind/rain/snow, the shell layer isn’t really necessary.
If you’re outside, it makes a big difference since wind can go right through most insulation and base layers.
For lifting in my garage, most of the time I just use a middleweight base layer on bottom with jeans over that, a lightweight base layer on top, then wool gloves, wool hat, wool socks with boots over the top. Depending on the temperatures and how warmed up I am from my workout, I’ll also use a middleweight layer on top and/or a fleece jacket.
Over the course of the workout, I usually just end up with the lightweight top. My middleweight layer is a fleeced polypropylene.
The other day when I was lifting in -10F windy weather with the garage door open, I was wearing a lightweight and middlweight top and bottom, fleece jacket, jeans, softshell jacket, wool gloves with fleece mittens over them, a wool hat, wool/nylon socks, and a pair of heavy boots. This kept me warm, dry and comfortable. I don’t need nearly as much when it’s 20 or 30F.
A military surplus store is a good place to look for things if they carry any ECWCS or ECWCS GEN III tagged clothing. The prices are going to be cheaper than most other stores for basically equivalent stuff. Even then, it’s not cheap.
Probably most importantly, try to avoid wearing cotton, since it collects moisture (sweat and water vapor), and will keep you cold. This is especially important when you’re active in the cold. If you’re going to wear cotton, try to make sure it’s as close to your outer layer as possible. E.g., undearmor base layer, then wool sweater, then cotton hoodie/sweatshirt. If you’re outside, you can then wear a lightweight rain jacket/windbreaker over that.