This has a list of DietPi's pre-installed applications and the packages that it has available for installation: http://dietpi.com/phpbb/viewtopic.php?f=8&t=5#p5
my device connects to any hdmi enabled tv and provides a digital scoreboard for sports, basically i'm running a chromium browser (via electron) and autostarting that when the device starts. the device is then controlled by an ios app. i ended up using ubuntu-mate, but i don't think i even need gnome, maybe something along the lines of windowmaker, flux, or lightdm would do. i need to save microsd space so that i can have users upload media like images and video, and ubuntu mate really hogs up 4G and above which forces me to have to supply a larger microsd card which ups the total cost.
The most recent image I built ended up being around 700MB, but I included some stuff you may not need, so you might be able to get that smaller.