Generally use automatic weights for the main part of the model and add smaller details later with manual/automatic weights or projected weights.
For the helmet you can manually add it to the head bone with vert group with 100% weight and that should be good enough.
This is how you can project weights.
If you have the main parts of the model weighted correctly adding clothing details like this is good option as automatic weights only tend to work well on single continious meshes with no breaks. For complex stuff it’s sometimes faster to create a additional low poly mesh only for weight painting and then projecting weights from that to the actual meshes.
Sorry for rambling on a bit. Trying to sum up: Automatic weights doesn’t handle separate parts well. Split your skinning process to separate parts and use different methods to get good weights and join them up afterwards.