Davey,
I stopped at Burgos last year and will resume there around mid May this year; we might meet. I will try to give you the benefit of my humble experience in replying to some of your questions.
Footwear : I have a pair of North Face ankle boots and I reallyappreciated them. When walking on flat surfaces there are no problems with any shoes I suppose; however, at least up to Burgos, the roads are quite tough, rocky and with a continuous "up and down" motion. I was quite surprised by the steepness of some down hill portions, amid rocks and boulders, I REALLY appreciated a good support around the ankles. You might carry a pair of good sneakers to walk gentle parts of the Camino or to help heal an injury.
As to socks take them with quick dry qualities as drying them overnight is sometimes difficult because of rain or air dampness.
Backpack : 45 l is perfect. Remember to practise loading and unloading your pack at home; this will assist you in refining its content and in eliminating unnecessary stuff.
Sleeping bag : Once again I have a North Face (0°C); it is extremely light and in October last year I was never never cold. Weight is of the utmost importance as you may wear more clothing as it gets colder, as opposed to bringing a woolen blanket of several kilos.
As to prices in Pau or St JPdeP I cannot assist you. Pau is a large city and you might find sports equipments shops. In St JPdeP, it is a beautiful but very small town. I am not convinced you will find the equipment you may be looking for. You will have more luck in Bayonne which is a large city.
Buen Camino. You will love it, I am anxious to return to Burgos.