Jodhpurs and Breeches
You'll find ordinary trousers and jeans rub in some very tender places and the purchase of a pair of jodhpurs or breeches will bring welcome relief.
Traditionally breeches are cut with a leg that stops around the calf area and are designed for wearing with long boots. Jodhpurs are made with a longer leg length and are suitable for use with short boots and will usually also be fine with long boots.
There is a large choice of specialist jackets available from many suppliers. They have been specially designed for riding, especially in the cold and wet, are cut to be 'saddle friendly' and some come with detachable linings so you can adjust them to suit the climate.
If most of your early lessons will be spent under cover then something simpler will do to start with. The main points to consider with a jacket are,
I use a cheap fleece type zip-up jacket that seems to work well for most conditions. Although not waterproof, it does dry quickly and being cheap it doesn't matter too much if it gets chewed, and when the horse decides to wipe his mouth across your arm it is easily washed.
Useful for keeping the cold out and your hands clean. You'll need a pair that allow you to 'feel' the reins and will not slip if wet. I personally don't use gloves except if it is really cold or wet, prefering the direct feel of the reins - the price I pay; some hard skin on my fingers and dirty hands.