So many people starting out in electronics, especially beginning to dabble in the world of Arduino and similar boards, just don't have the basic equipment to do the job properly. And not only that, they don't even know what the basic equipment is.
So here's a list of things you should have on your desk no matter if you have just got your first Arduino or if, like me, you are a seasoned veteran.
Invest in a good pair. You'll find it's worth the extra cost. The big bulky ones you get in general toolkits aren't great for electronics. You need something with a good fine end to them to get into those tight spaces.
Please, don't use your teeth! I have, for many years, and now I have a notch in my teeth. Stay away from cheap "notched scissor" type strippers and invest in a proper set of mechanical gripping strippers. The results will speak for themselves.
Not all soldering irons are created equal. You really need a temperature controlled one if you are to prevent damage to your electronics. On top of that, if you can afford it, get one where the heating element is contained in the tip of the iron not the shaft: these heat up much faster and hold their heat better.
The number one most important piece of kit is the digital multimeter. It combines most of the functions you will need on a day to day basis in one simple to use device - ammeter, voltmeter, resistance, even sometimes capacitance and inductance. You really can't live without one.
For closer inspection of signals you can't beat an oscilloscope. Entry level digital ones now are reasonably priced, but if you don't mind something somewhat heavier you can get some great bargains on old analogue oscilloscopes on eBay. More functions for the same price, just somewhat heavier and can be more tricky to use.
Full featured logic analysers can be very very expensive. However your PC makes a great logic analyser if you have the right dongle. And you can get some really cheap on AliExpress. For example this one, which works really well with Sigrok.