OLED is a good idea. 96x16 is equivalent to 16 characters by 2 lines (with 7x5 pixel characters). I see plenty of 128x32 pixel OLEDs on ebay (or wherever) that would give you 21 char by 4 lines or fewer bigger characters (say 10 chars double size plus 2 lines of 21 chars, etc.).
You don't need anything nearly as powerful (or power hungry) as a Raspi, instead you can use almost any cheap small microcontroller like a Arduino nano clone. It just needs to parse the serial data stream coming from the GPS module of our choice, and present that information in some meaningful way to the user on your display of choice. It's a relatively simple task. The 128x32 OLEDs are usually based on SSD1306 controller, supported by u8glib on Arduino which makes short work of writing information to the display.