amateur question on GPS receiver

Hello!
I learned about Arduino some weeks ago at university and now I am at the point where I could perfectly use it for a project for my degree.
Before starting I wanted to make sure if my idea is possible to realize and not too hard and time consuming:

My device should tell distance and directions to a fixed destination, if possible when switching it on the should be some kind of selecting on out of 5 or so programmed destinations.
It looks like this: http://cl.ly/image/0J1B1T0A1k44
and the idea is to calculate the distance with the GPS data and the coordinates of the destination by using a and b in the triangle.
Further the direction should be indicated by the LEDs around the compass above the display. I thought this could be done by programming different ratios of a and b to make certain lights shine.

Is this possible using this GPS receiver: http://www.oomlout.co.uk/gps-receiver-mtk3339-p-280.html and this Display: http://www.oomlout.co.uk/lcd-display-16-x-2-p-212.html

I know it might seem like a bad version of a proper GPS and you may ask why I just dont use my iphone. THe difference here is that the user does not see any streets and guiding route on a map and there fore develops a better awarness for driections and distances in his city.

Thanks a lot for your help in advance,
all the best from london!
leon

This page has info about how to calculate both the bearing and distance given lat/long.
http://www.movable-type.co.uk/scripts/latlong.html

Pete

Thank you pete, that's great!