Don't be overly concerned with safety. The best safety device is your brain. And I disagree that spending more on a meter will get you anything tangible. In the old days you could save money and get an almost worthless VOM at 1000 Ohms per volt but that's not available today. The cheap meters all have at least 1 Megohm input resistance, plenty high enough for most work. And more accurate than you will ever need.
When it's time to get serious with electronics, the meter will still be useful and you will want more sophisticated instruments such as signal generators, oscilloscopes, LCR meters, variac, soldering tools to add capability without obsoleting the little meter.