What to use to kill bushes and weeds around the house fence?

I would dig it all out (be careful with the poison ivy), and treat the ground. I use vinegar or Epsom salt.

I use this DIY Weed Killer or boiling water: https://thekitchengarten.com/diy-weed-killer/

Brush Killer, but do not allow it to drift to areas of preferred plants, lawn, trees, etc.

I would cut it all down first then apply the brush killer. As long as the cuts are fresh the brush killer will work. You might have to apply a couple of times. Like the post above be careful with the wind.

Brush killer is toxic and poison to all of us, a more natural way would be to mulch it with black plastic or black landscape fabric topped by something you want like regular mulch or pavers, Etc.