Which setting to use to measure exact voltage with this multimeter?

First make sure you don't touch the metal part of the probes as you don't want get a shock.

As to the needed settings for this meter: You want to use 200 volt setting for US (120 volts) and you want to use the larger 600 volt setting for EU (220 & 240 volts). Don't alter the dial while you have the probes in the socket.

This meter may not be the best choice and you may find the issue is not so much the voltage but the stability of your power, it's correctly wired as well as has proper grounding. This Receptacle tester is all you really need for quick testing. If you think you are having issues (beyond incorrect outlet wiring) I would strongly recommend you contact your power provider they have a power line recorder which they can place on one of your outlets to monitor the power coming into your house. Otherwise a local electrician can come in to repair poor wiring.

If the power is not stable I would recommend using a good UPS as they can smooth out erratic power and if you do get a brownout a good unit can back-fill the needed voltage as well as protect your equipment from a surge.

While that would be best it is not very portable (as you talk about going to Europe). To offset that I would recommend using a laptop Vs a desktop system as the battery & charger will act like a UPS. Even still you do want a good surge protector (not a power strip).