My recommendation would be, if you want to do a project that's engaging to you and that can look truly original in your portfolio, think of solving an issue that you have on a daily basis ! Most probably, a lot more people have the same issue and your project can become really useful with time :)
Dinesh recommends the following next steps:
So I wrote a small infinite-precision arithmetic library that could add/subtract/multiply/divide mixed fractions, the used it to write a matrix manipulations library that could perform similar operations on matrices of mixed-fraction numbers. Since we were required to show our work, I made the program print out intermediate results on the way to the finished computation.
My homework was reduced to a simple matter of typing in each problem, then running the program and printing out the results.
About a month into the course, I confessed to the teacher that I was doing my homework on the computer instead of working it out by hand. He didn't seem concerned, as it generally requires a higher level of understanding to write a computer program than it does to perform the same calculations manually.
The best way to learn programming is to solve a real-world problem that you care about.