Grid and background settings for new files can be set in Edit > Preferences.
You can set your default palette by loading or creating a palette and then clicking “Save as Default Palette” in the palette Options dropdown. I don’t think there’s a way to set default foreground and background colours, Aseprite seems to always use the same palette indices you used last time, regardless of palette.
Some users have reported issues with their grid settings not being used correctly. If that’s the problem you’re experiencing, this thread might be worth a read:
If you’re running into this issue, until it’s fixed, an option would be to create an empty template .aseprite file and load that in and resize it instead of creating a new document every time. This file will have your grid, palette, etc options saved.