Weld or replace?

[Velcro]

So I got a good peak under my car about a week ago and the exhaust is not in good shape in general. Mostly it's the hanger that holds the exhaust at it's midpoint to the car, but also where the exhaust manifold connects with the rest of the exhaust (sorry if I am mixing up parts). I have no experience with exhausts and am little above an oil change when it comes to working on cars, so I rely on other people for advice most of the time. Anyways, I've had mixed responses when I have asked what I should do. Some people say I should weld the exhaust back together, while others say that I (or whoever is working on the car) will blow holes in it and will need to replace anyways.

So should I weld the exhaust or should I replace it? If I need to replace it, please recommend a good place to get a stock exhaust or a good custom exhaust (I live in Virginia, so strict noise limitations). My car is fairly rare around here and I can't find a used exhaust at the scrap yards.

Thanks in advance.