You can obtain “VISA” to Nepal through embassy or other diplomatic mission to your country. You can also obtain visa at entry points to Nepal, or at the airport in the immigration for merely $40. The extension of visa requires an additional payment of $30. Do not forget to carry some passport size photos with you.
Everything you want to do is time and cost specific. Besides, your experience in trekking will also matter. There are wide range of options in Nepal if you want to explore. If you arrive in proper season, that is, between September to November (Autumn Season) and March to May (Spring Season), you might just experience something that you will be able to cherish for the lifetime. The shortest of trek can be Ghorepani Poon Hill trek, Langtang Helambu Trek or the Annapurna Circuit. The Everest trek and the full Annapurna sanctuary Trek can be ideal if you have a little more time. Finally, if you are looking for something that’s longer and more challenging, you’re looking at Kanchanjunga or Makalu area Trek.
Annapurna Circuit, Annapurna Basecamp, Everest Basecamp, Dhaulagiri Circuit, Manaslu Circuit and Kanchanjunga are the most popular trekking routes in Nepal.