If you're searching for the perfect Vim TypeScript plugin, then there's a new one called Tsuquyomi (GitHub: Quramy/tsuquyomi, License: MIT) by Yosuke Kurami. It uses TSServer, which comes with TypeScript, and provides omni completion, symbol navigation, compiler errors, and identifier renaming. It requires vimproc, which is used for asynchronously executing commands.
For most TypeScript programmers, Tsuquyomi feels like a complete solution. The documentation is pretty good, so as long as you can install TypeScript and vimproc you should be able to get it working.