You want your closing statement to be the Mariano Rivera of letters of intent: a clean win, effective, and unambiguous. Don't overthink it! Basic, professional closings are the way to go.
Without job-level specifics, it can be tempting to get stuck in an "I'm awesome" loop without giving enough specifics. If you have a general idea of what job groove you'd be seeking at this particular company, build your letter body around that. If you're truly just trying to get a foot in the door at a company, you can use clues from your research about the company. What does their website say about their mission and priorities? What do current and past employees say about the company in online chatter? Even without specifics, you can cobble together a pretty good idea of what the company is seeking in potential employees. Sell your skills and experience points that are special to you, and especially relevant to your industry.