After your raincoat, the most important item. Don't go far from the car without one in Tasmania. Most walkers these days use polyester fleece jumpers (Polartec or similar). A good warm woollen jumper will be quite adequate too, but for equivalent warmth is slightly heavier than the polyester fleece.
Importantly, jumpers made from cotton are NOT suitable. Once these get wet they are entirely useless in keeping you warm, and dry very slowly.
While considering the upper part of your body, you may also find it more comfortable to walk in something other than cotton shorts. These get damp with sweat and stay damp. Polyester, or other "plastic" clothing for both warm and cold conditions is much more comfortable.
Many people walk in shorts, even in cool/wet weather. As one friend of mine says, "skin's waterproof". The normal approach of regular walkers is to wear shorts until it gets really cold, and then to just add thermal leggings worn under the shorts. This admittedly looks daggy, but who cares?
If wearing long trousers, you are strongly advised NOT to wear cotton trousers. This includes especially jeans and any others made of heavy cotton material. Once wet, these are uncomfortable, difficult to walk in and impossible to dry without a roaring fire. In a cold wind they become dangerous by drawing heat directly from your legs. If wearing cotton, make sure they're very light. They'll get wet very quickly, and dry just as quickly. better still, get some polyester "outdoor" pants. There are those ones from which the lower legs zip off to make shorts. At least get some "microfibre" or similar track pants. They're better than cotton.
Warm hats come in many forms. In cool months, they are vital just about anywhere. The body loses a lot of heat through the head. It's amazing how quickly you cool down once you stop for a rest or lunch. A good thick polyester or woollen beanie is sufficient to start with. You may later decide that a balaclava and/or windproof fleece hat may add to the versatility of your wardrobe. Various hats can be added together to deal with particular conditions. A cap or sunhat is NOT sufficient in cold weather.
After the head, the next most important area to keep warm is the hands. These lose a lot of heat, and become very uncomfortable. There is an amazing variety of gloves in the shops. The woollen ones with a "Thinsulate" lining are quite adequate for most things. If you expect rain, I strongly suggest having some waterproof overmitts, as gloves rapidly get wet (and virtually useless), especially if you are having to contact rocks or undergrowth. There are some very nice "glove systems" around, but expect to pay $100 plus.