At 320 lbs your biggest concern will be the wheels. You will want 36 spokes minimum on the rear wheel, and a decent double walled rim (Velocity Deep V are a strong rim and would be a good choice). Also, it's worth learning how to true a wheel/replace a spoke, they loosen up more frequently with heavier riders.
It's probably a good idea to get into the habit of raising your ass off the saddle when you go over bumps on the road. Besides being much more comfortable for you, this will radically reduce the chance that you bend the rails under your saddle.
Get a good floor pump in your garage with a gauge and remember to check your tire pressure and pump your tires up before each ride. It only takes a couple seconds, and should be part of your routine. Your chance of pinch flats will be much higher due to weight, and it's annoying to constantly be changing out flat tires.
If you live in a hilly area your chain and cassette will wear a little faster than for a really light person because it takes much more power to climb. Again, if you live in a hilly area you will need more braking power to stop, so should keep an eye on your brake pads as well.
Other than that, you shouldn't have any problems with wear from your bike. Frames are hella strong, cranks are very strong, your bars can take a lot of abuse, and as long as you keep an eye on the stuff mentioned above you'll be out there pedaling away and having a blast. I've known people who lost a ton of weight cycling, so it may not even be a concern for too long . . .
Final bit of advice . . . don't buy a bike at Walmart. They tend to be made of poor components, and aren't assembled very well. The frames are often very heavy, so even if you start upgrading things it's not really worth it in the end. It might be a 100$ purchase, but the cheaper components will need tuning more frequently, the wheels will probably not hold up for very long, etc.
If you want to get started the cheapest way possible, look for a used hard tail older mountain bike without a front suspension. They tend to have pretty tough wheels on them, be cheap, and you should be able to find one that's better quality than a Walmart bike for 1-200$. If you replace the tires with some slicks (probably set you back about 40$) they'll roll pretty well on the road. Mountain bike gearing is easier than most road bikes, so you'll save your knees when going up hills.