I have been a licenced marine tech for over 30 years, and have accumulated over $40,000 in tools required to be efficient in my trade. This does not include tool storage units (another $8,000), manufacturer specific "speciality tools", or computer diagnostic tools. I won't bother itemizing general tools, you will figure out your needs the first week on the job, but here is some general advice:
Start with good diagnostic tools. If you don't know what the fault is, all the tools in the world wont help you. A multimeter with a DVA adapter is essential, as is a dial indicator set, timing light, a multiple cylinder spark tester, a fuel pressure and vacuum tester, and an accurate shop tachometer. And don't forget a set of torque wrenches. And the list goes on!
A good tool storage system is a must. Keeping your tools clean and organized helps keep you efficient. Make sure the cabinets and chests can carry the weight of the tools. Ball bearing drawer slides and casters, welded cabinet construction, and solid work surfaces are some plusses to look for.
Buy good quality tools once, rather than cheap junk over and over. Try not to become brand-fixed: even the best tool makers have lemons in their line-up. As an example, almost all my sockets are from Westward, and are of a better quality than Snap-On, and at about 1/3 of the price.
INSURE YOUR TOOLS! Keep them locked up when you are not around, and don't loan them out.
If your tools are lost, stolen or destroyed, you are out of work.
Ask advice from older, more experienced techs you work with. Most of us old farts are more than happy to offer advice as to required tools, brands, good deals, etc.