Mahogany definitely has more grain than Basswood.
If not too late don't over do the sanding on back, sides and neck as you want something for the timber mate to get stuck into, therefore 120 or 180 is plenty. 24 hours after timber mate has been left to dry is when you start again with the grit you finished on and work upwards to 240 to really smooth things out. Depending on grain definition and what you will use for staining 240 may be enough but no higher than 320 if you want any colour to really soak in.