Take a look at the rather slim linux distributions specialized in embedded systems, like firewalling distros and so on.
Then, if it is a graphical application you have to make sure you boot into runlevel 5 (graphics) and configure your application as login shell for the default user.
You might also be interested in two services the openSUSE project offers: the Open Build Service (OBS) and SUSE Studio:
OBS allows you to automatically get packages of your application built and packaged, ready for use in a number of wide spread distributions.
Studio allows you to go a step further and create a custom distribution for your own purpose: you can call it 'your' operating system, completely preconfigured for your purpose, with all requried software and your own application installed. You just have to download a CD image afterwards!