When you go through a publishing company, they have professional editors and staff to promote your book.
It might be more impressive to attempt to go the regular route for publishing a book – attend workshops for writers, read some of your work at local bookstores or where ever these readings take place, contact editors for various companies, prepare a prospectus or send a few chapters. In your application, you could describe your progress with this. It would be odd to self publish a book without trying to learn what real writers do.