Sub from Wizard
You may start your sub-path to any class you wish, however the most common wizard sub-path would be to priest. This will make you a "Wiest" (Wizard-Priest): which basically will be a priest with fas nadur. When planning for subbing, you must be very careful with your stats, make sure you will be able to learn all the spells you wish to learn before you reach 99. Council the spell and skill sections for information of stats to learn spells.
When subbing make sure you are wearing the right gear to give you the most advantage in your new path. A dark belt and stone axe are most of the common helpful items to start you off.
Sub to WizardIf you have arrive to the wizard path via subbing, you already know most of the basic information to start you off. You will be given a weaker form of the Grand Master equipment and will not be able to learn Wings of Protection or Lyliac Plant when you go summoner. These are virtually the only drawbacks you will encounter on your path as a wizard. Good luck on your new path.