I am a junior software dev at a small software company. I can't really get anything from my company in terms of advancement as there are people in the way so I will need to leave in about a year. There is no real opportunity for additional responsibility either as the project scope is very fixed for our client. What are the best ways to build my resume outside the company?
Start building your resume with whatever you do in the current company. That is probably the best you can do. Even if there are not big opportunities, try to get involved in more than you already do. That will help building your CV.
(idea) Start your own company.
(idea) Find another job, do not wait too much in a dead-end job.