A Skills section is usually for the purposes of an ATS (automated resume scanner) or a human that will be looking for certain buzzwords, like a language or a framework that is most important to the job requirement. Recruiters know they can go to a skill section and find those things quickly.
I think in your situation, listing specific examples of your accomplishments is going to be even more important. You can tell me "I'm an all-around developer who cares about getting things done..." all day long, but listing specific things you've developed to illustrate that point is much more effective. It's not unlike people who say they have excellent communication skills - don't tell us, show us by writing something or demonstrate it in conversation.
Recruiters and HR are looking for those buzzwords, but engineers reviewing the resumes are looking for an interesting project that they can ask you about. Ideally it will involve a problem the company is trying to solve.
Start with a summary to quantify your experience - this starts the reader off with a big picture of who you are. Don't trust the reader to figure out you're a full stack dev, because the person first reviewing your resume might not be technical at all. They need to be told specifically what you do, and it's your job to do that. Your summary might start "Full stack developer with n years of experience across a mix of languages and platforms in Agile/TDD development environments. Additional skills in Project Management..." or similar.
Next, experience section with responsibilities (the day to day) in a couple sentences in paragraph form, then bullets for your novel accomplishments.
Skills, Education, other projects, community involvement, etc. to follow.