Yes run to the battery and ground the negative wire NOT on the battery post but nearby on the frame where the other grounds go. No need to put a fuse in it. If possible do NOT connect to the positive battery post either. There is probably a good solenoid nut or master switch where you can get some distance from the potential corrosion issues of connecting directly to the post.
With rusty chassis' and poor ground connections I recommend to NOT ground a 100 watt radio to anything nearby. A low power radio is less likely to cause any RFI issues. Most high power radios we install come with long positive and negative leads.