I am a fan of trekking poles/hiking staffs and have used them consistently for about thirty years. My experience is that this is one area where you can save money and not cut utility.

Worthwhile, cheap expedients include the replacement tool handle from the hardware store (or the even cheaper broom or rake, sawn to your specs), and the right sized limb picked up along the trail.

The fancy schmancy telescoping poles can come later. I do have, and use, a nice pair of Leki's. They have their virtues - light, collapse down for easy packing in boats and planes, make good tent poles, etc. The cheaper alternatives work just as well on the trail and in stream crossings. My all time favorite staff is a natural limb discarded by another hiker which fits my hand perfectly - just great for day hikes, and it is quieter than the swanky ones.

I agree with the advice to get a good down bag - absolutely fundamental, useful gear. I would advocate going over budget and getting a really warm, light bag. You will be glad you did.