My advice is to stay more then a month in rented apartment, or even whole year round, so you can understand how it looks like in different seasons.
Some places are nice at summer, but very hard to live at winter, some places are nice to visit but very depressive to live there, like Kotor old town, everybody fall in love but to spend winter with almost no Sun, and with this sewerage smell, no body can do it.
Currently for most of foreigners Tivat is most popular, but prices age growing over there. Bar and Ulcinj areas are cheaper then northern part of coast.
Internet connection can be problem, but now there are more companies offering different type of internet, so this is good now. If you want to live close to the coast, you should see is it crowded during summer, if you want to live higher in hills, you should sea how road looks like. Unstable electric power supply can be a problem too.
As I said, my advice is to live here and there for some time, apartments are easy to find out of summer season, and then to choose where to settle down, and if option to buy flat or house....