I'd wait to see what the course tutor recommends as there are a number of options that I wished I had and don,t have! For car electrics you'll need something that'll accurately give you at least two decimal places for checking the state of a battery or charging circuit, but at the same time you often only need something as simple as a lamp on a lead for checking if there's a voltage there or not rather than waiting for your super expensive Flike or Avo to auto range thro! I have an all singing all dancing Avo that does Capacitance and frequency (never used) as well as DC/AC voltage and Amps, but does not have a temperature feature that I feel is essential for car electrics and maintenance. For example you can check glow plug function with a temp gauge by placing the prob on top of the glow plug or check auto box oil temp before taking a level reading etc. For me its not so much about the name, but the functions that I want. Its also nice to be able to take current reading using a clamp meter, but not all current clamp meters will do DC amps!!!
I think to cover all possibilities your best off with two or three separate bits of kit. This also builds redundancy into what you have.
1 x Simple Lamp pen with a lead and a crocodile clip
1 x Good quality Volt meter with Amps, Continuity and Temperature functions
1 x Good quality AC/DC Current Clamp meter (this will also likely have the ability the be used as a Volt meter and so provide the redundancy)
1 x Large safety pin (I use one of these to see whats going on inside a wire without seriously compromising the insulation by just gently piercing through)
1 x three meter long wire with a crocodile clip on each end for extending the length of a prob lead
This would be my perfect list if starting a fresh
