Hmm.. I really like the starting hand stuff. But if you say you don't have that much time, lets break it down a little.
First of all,
forget about a fancy interface and such, start on the console.
Then I would suggest to build a program, that reads a given deck list (just a simple txt file), writes them into an array (preferable each card n times, there n is the amount of the given card), shuffle it (I'm kinda sure you don't need to write an algorithm by your own for start) and print the first 7 items of your array afterwards.
This should be doable even with a limited amount of time. After you've got this basic construct, you can add future functions, like a simple user interaction for drawing another card or shuffling again.
In general, if you want to learn programming, start on the console. first learn how to make stuff work, then learn how to make them look pretty.
If you're starting with the UI, you'll usually spend alot of time designing it and moving stuff pixel wise, in stead of doing the real work. That's at least my experience.