For a jacket I’d recommend a down puffer jacket. You can spend $300+ on one but I’ve had great luck with the $30 ones from Costco. Amazon also has a good selection of sub $100 puffers.
Medium weight fleeces can be found anywhere- Walmart, old navy, etc. I got my main fleece for four bucks at a thrift shop. A wool sweater works just fine too.
Rain jacket is tougher. Frog Toggs are cheap but loud and not super durable but get the job done. This is one where you largely get what you pay for. Will she be doing much physical activity/sweating? Ventilation zippers help a lot in that situation.
Winter hat? Too many options to list. Use what she has already. I usually carry a lightweight beanie and a heavier warmer hat when I’m backpacking so I can switch based upon temperature.
Gloves depends upon what she’s doing- will she be working? I’m partial to insulated soft leather work gloves, but if and when they get wet they take a lot longer to dry. Usually I only take a light pair of poly gloves in the summer unless I’m doing trail work.
I highly recommend the Kelty cosmic down 20 sleeping bag. It’s down, will keep you comfortable to about 30 degrees (lower if using a bag liner or wearing extra clothes), lightweight and packable enough for shorter backpacking trips, and is less than $110 on rei right now. The poster that recommended a 0-10 degree bag is way off, she’ll be burning up in the 50 degree summer nights unless she’s a really cold sleeper.
Pad? Could go as cheap as you want but I like a decent backpacking air mattress. Quality of sleep directly translates to quality of life. I’d try to check them out at a physical rei or other outdoor store if you can since it’s largely a personal preference/sleep style. Sea to summit, therm a rest, big Agnes, and Nemo all make quality pads. There’s a basic Nemo pad on sale at rei for less than $55 right now.