The multimeter is perhaps the most important test instrument in your lab.
If you are just starting out, it is easy to be confused, not knowing how to interpret the differences between the multitude of features that modern multimeters offer.
I’ll try to make getting your first multimeter easy for you. I would go for an auto-ranging multimeter, like the INNOVA 3320 Auto-Ranging Digital Multimeter. It is well priced for the features it has.
With auto-range, you don’t have to worry about worry about choosing the right scale for the measurement, your meter will figure it out automatically. It takes a bit longer for each measurement (still, less than a second) but saves you the hassle of playing with buttons and dials. Such meters also tend to be better made, with proper fuses and will last a long time.
As long as your meter can measure DC voltage and current, and has a continuity feature for testing short-circuits, you will be able to make 99% of the measurements you need around your Arduino.
NEVER try to measure mains with a multimeter unless you know definitely that the meter is designed for that and is properly fused. Minimum certification for AC mains measurements should be CAT IV.
If you are looking for a more high-end (and expensive) meter, look at the Tenma 72-7730A. It has very high accuracy, true RMS (good for AC measurements), you can connect it to a computer for remote measurements, has a data logger etc.
In our course The Electronics Workbench: A Setup Guide, you can learn how to use a multimeter, as well as other test instruments like the osciloscope and the signal generator.