Anyone from the West can get a 120 day tourist visa upon arrival in Armenia at any border. It’s 10,000 dram (under $30US). If you plan on living in Armenia however and you have at least 1 Armenian grandparent, you should apply for either a 10 year residency or Armenian citizenship. You should apply from either your home country 4 or 5 months before departure, or immediately upon arrival in Armenia. The application process takes approximately 3 months, but can vary a fair bit in either direction.
The process for the 10 year residency visa and the citizenship are almost exactly the same. The 10 year residency must be renewed after 10 years, whereas obviously citizenship does not. The costs are also similar, in the $300 range. The 10 year residency gives you everything citizenship does except the right to vote, and the obligation to serve in the military if you are a young man. With either one you can buy land in the country – without either you can only buy buildings and apartments, and lease land.