I forgot to mention that if you get an auto-ranging multimeter, make sure that it can also be set to manual mode as well.
In addition to a good accurate digital multimeter is is worth considering a half-decent, but low-cost analog multimeter which would be useful for watching varying parameters, like the voltage across a charging capacitor for example. The bar-graphs on digital multimeters don't have the same 'feel'.
When choosing a multimeter concentrate on the accuracy and ranges of the three basic parameters: DC voltage, DC current, resistance, before the fancy facilities like diode and transistor testers. Particularly consider the high and low end values of the parameters you will be measuring.
At one end there is your mains voltages and currents and at the other end there are the quite small values in modern electronics. For example the 200mV of a forward conducting schottky diode and the 10uA of a small-signal transistor base current.
I am not necessarily advocating a Fluke, and especially not at the low-cost end where you can get better value for money elsewhere but, apart from being nice instruments, Fluke always have a reasonable resale value.
And remember, a multimeter is not just for measuring electrical values, it is a treasured possession for many of us.