As you'll get more levels, you'll get more skill point per level (2 per level, then 3).
Zombies have huge resistances (they bleed poison AND heal from it, they have piercign resistance whichis good against marksmen and scoundrels).
If you find the starter weapons are better than your current weapons, use them, otherwise just stock them somewhere waiting for the upgrades. Be aware that even though you can wear weapons that are above your level, they incur AP penalties.