First of all, since UK is not part of the Schengen Area, it would make sense for you to get the UK visa first. Assuming you have a Nepalese passport (GC doesn't matter), it's advisable to apply for the Schengen visa in advance as they are pretty thorough in checking every detail(yes, even for casual tourists).

As far as applying for Schengen Visa goes, if you're not located in Washington DC area, you have to appear in one of the local consulate offices and provide all the necessary documents. You can either pickup your passport or have it posted (not advisable!) in a week or 2. Hope that helps.

Jai Nepal.