I am American, and I just hold my American properties as a single proprietor. An LLC gives some protection from liability, but it has to be carefully maintained. To me, it's just easier to keep adequate liability insurance and keep the maintenance done on my buildings so they are not in an unsafe condition.
I have no idea what sort of holding companies you might have available to you in Europe.
I suspect your chances of getting a mortgage are non-existance if the money isn't borrowed either in your own name, or in a corporation that is old enough to have established it's own credit rating and has adequate assets to cover the mortgage.
LLC (in the states) is transparent to taxes. You pay income tax like the LLC doesn't exist. Corporate taxes are very different and you need to get a good accountant who specializes in real estate to explain the ramifications to you.
My opinion: some of the places that are extremely cheap and heavily promoted in the States are not good places to invest. Look for a town that has jobs available for the local population and a sound economy. It's a big country and there are lots of really good places to own real estate. Avoid like the plague any place where most of the population is living on welfare.