You could provide the packages yourself, but that's not the ideal way to distribute your application. Users won't be able to find your software in their distribution's package repository and will have to hit your website to download the latest version.
IMO the best thing to do is solicit the help of package maintainers for the distributions of your choice. Get one of them who is interested in your application to adopt it and bring it in to the distro, then they can take care of the distro-specific details of packaging it.
Your role will be to assist them as much as possible in getting your software to build on their platform and work out any bugs related to interactions with other package versions, etc.