I think the Uni-T 139C is a good choice for you. With it you have the ability to easily access the small fuse. When you buy a meter, also buy a set of fuses in the right size. You may need them one day.

In case of the Uni-T 139C that is: 6x32 mm FF 600mA H 600V (according to manual).
EDIT: About safety and mains, here is how I see it:
Every Phasenprüfer for 1 Euro is more "unsafe" than your multimeter. When people say, "the meter is not save on mains", this does not mean that it will automatically turn into dust when you measure mains with. I read the linked article above: it basically says, that you need to be careful and that a good quality meter doesn't protect you from main, but it helps to protect you a little bit from your own stupidity. I ALWAYS treat mains with respect. I plan every hand move very slowly and don't take any risk, when I work with it. And you should too – but most of all: don't be afraid, or you shouldn't do it at all. Don't be too concerned about CAT ratings, they don't protect you from your own stupidity. Such a meter is ok, when you occasianally want to work with mains. Should some day come and you find yourself working on mains routinely on a daily basis: then by all means get a very good meter, that is suitable for this kind of job! But for now, I only can say: I measured 15A 240V with my 25 Euro Multimeter VC97; I'm still alive and so is the meter.