score:5
Apply for the Schengen visa first, and have it in-hand before you apply for the UK visa.
As to the Schengen visa application: you're already re-admissible to the US with your F1 status, so you won't have to convince the Schengen authorities that you can depart when your visit is over. Schengen won't care how you get to your Schengen country of entry.
As to the UK visa application: after you have the Schengen visa, apply for the UK visa. UKVI will (among other things...see below) be concerned that at the end of your visit to the UK you'll be able to leave the UK. Having already obtained the Schengen visa, you can show UKVI that you'll be able to leave the UK when your visit there is finished.
This application order best supports your planned itinerary by showing you have the legal authority to leave both the UK and Schengen after you visits, and travel to the next destination. These points do not, however, address the major issue that arises in visa applications: that you will, in fact, depart when you say you will. This issue should be addressed by you demonstrating that you have (in the US) something important and compelling so that so that you'll not go underground in the UK or Schengen area and and thereby remain past the term of your visa.