I need help planning a trip to Bhutan, Nepal, and/or Tibet.?

My friend and I want to go for about a month or two to these countries during next summer. We would like to see some of the following: potala palace, Paro Taktsang, the himalayas, and Katmandu. We have a limited budget and each have around 2000-3000 dollars. I don't know if this is enough but volunteering is a possibility. Im also not sure about how travel visas work. We prefer to travel independently but it may be difficult so we are also considering travel tours or travel agencies.