For the mentioned tasks, you probably will rarely have to use Amps measurement, so the emphasis would be on reliable Volts measurements. For electronics, also diode test and some capacitor checks.
Safety-wise, if you work on mains voltage, you should look for a CAT III 600V rating, AND for probes that are CAT III, meaning short exposed tips.
Everything else is CAT II territory, where any good quality gear will do. Uni-T 139 would come to mind, but those are reported to be a bit sensitive to misuse like getting voltage when in Ohms mode... Otherwise it should be fine. For probing mains (especially for the absence of voltage) a multimeter should not be used, only a 2-pole voltage tester like a Fluke T110 or german brand Duspol (Benning).
Measuring-wise, some sweet spot regarding costs is 6000 counts, but more important IMHO is the base accuracy of a meter- I have some old Fluke 8020 here, that has "only" 2000 counts resolution, but 0.3% base DCV accuracy, and still is within spec after 40 years- way better than some cheap new meters, that sometimes have less than 0.5% accuracy...
So, base DCV accuracy should be 0.5% or less, and counts more than 2000.
Important for testing LED: you will have to look at the voltage for diode test, here have lots of budget meters differences. To make a LED light up, you need a multimeter that can test diodes with at least 2V, better 3V- the latter mostly means more expensive gear. Some cheap meters only can use 1V, which is ok to test normal diodes, but would not make a LED light up.
A colleague at work has been provided with the Amprobe-510 and is not unhappy with it, but also had basic needs.
For a begin, it should be sufficient, and then there is one rule: You can not have enough multimeters, and they tend to reproduce. Means: in the foreseeable future, you will look for another one, and then you probably know which features you need, that the existing meter does not have.
Question here: What about used gear, like a Fluke 77 series etc. in good condition?