Residency in Armenia
Residency can be applied for either inside or outside of Armenia. If you have some Armenian ancestry, you are eligible for a 10 year residency visa, which costs about $300 and takes 2-3 months to process. The process is relatively simple and should present no problem. It is unclear whether these visas are issued to non-Armenians, I have never heard any information on this matter either way. There are also 3 month, 6 month and one year residency cards, which will cost much more than the 10 year visa in the long run. All of these visas give you a right to work. There is also a student visa for those getting an education in Armenia.
If you just arrive in Armenia with no visa at all, a 3 week tourist visa will be issued upon arrival for $30. After that expires, if you fail to get a longer term visa, you pay $3 a day when you next leave the country for each additional day you have remained. Depending on the length of your stay, this could be your easiest option.
Either visit your local Armenian Embassy for more information, or in Armenia visit the OVIR office off of Mashdots.