Since this is a rental and we do not know the lease terms... the landlord may not take kindly to someone taking on electrical/plumbing/repair & maintenance items on their own. Just MHO.
When our daughter went out on her own I gave her a bunch of free Harbor Freight (go HF!) tools and a few others. Hammer, level, picture hanging kit, tape measure, needle nose pliers, screwdriver set, set of quick clamps, putty knife, cordless drill/driver with basic bits.
Our son - I always bought him tools for Christmas & birthdays from the get go. He got plenty of toys from everyone else. He left home with a complete set of mechanics and woodworking tools