Moving to the Luxembourg

Hi There
i am a US Citizen living now in Eastern Europe with my local fiancee where we have our English school for teaching the language.
i am thinking seriously to move to Luxembourg so i need information to start my business and be well set in a flat / accommodation..

i appreciate all details about rent cost, session of tuition per hour in average .. and best places for this to start and of course living .

i also would be interested in how hard or easy to get residency or logistics to start in the country ...
all details would be perfectly appreciated ..

Frank
thank you in advance