Minimum requirements are listed here:
https://helpx.adobe.com/illustrator/system-requirements.html
In my humble opinion a good Windows-based notebook (for graphics purposes) would have:
• at least 32GB of RAM (64GB or more is better)
• a discrete graphics board with 4GB or more of GDDRAM
• at least a Core i7 CPU
• 64-bit Pro version of Windows, not Home
• 15" or larger display
• good selection of ports
If this notebook computer is meant to be portable and offer long battery life then the hardware configuration will have to be adjusted for that. It's a push and pull balance. No notebook computer is going offer thin/light portability with long battery life and brute force power in the same package.