Deciding which one to do....hmm....
Money would be one of the biggest factors. For the longer trip, you will spend more on fuel, food and lodging. However, there are people here who have managed to have wonderful trips on low budgets (but not too low), so we can help you with tips if needed.
Easing into road trips isn't a half bad idea. My husband and I had our first road trip together when we were newlyweds. It was all of 4 days long, and we enjoyed it a lot. (We were moving from MO to AZ. Both of us, however, had been on road trips with our respective families before we were married.) That made us want to do longer ones, and the very next summer, we road-tripped round trip AZ to MO. That led to a 3-week camping trip, eventually. You learn, on short trips, how much you can handle, what constitutes a nice driving day vs. a brutal one, and what kinds of things you personally require on a trip.
What do you want to do on THIS trip? If seeing your uncle is a priority, then I'd head that way. If seeing some beautiful scenery is a higher priority, then the Smokies and the Blue Ridge mountains would be the place to head for. And so on, and so forth.
An App for severe weather -- ooh, very good question. My husband and I travel with a CB radio in our vehicle, and we have the NOAA band on it. A couple of summers ago, we had that band going several times as we crossed through some bad weather in the Gulf states and later, in Kansas/Colorado. I believe there is an NOAA Radio app for iPhone, and an NOAA Weather Alert for iPhone, both free. If you are a Verizon customer, we have noticed that we get alerts from there on both our old Droid and our old Dumb Phone. (One was a dust storm likely alert, in Arizona, and another was a Flash Flood Warning in northern UT.)
Either trip, it should be a great one for you. Keep us posted on which you choose, if there's any more help we can give you -- and either along the road or when you get home, give us a run=down on your travels, in the Trip Reports forum. I love to read other people's Trip Reports!