It depends on your budget, whether you're after sound or performance, your tolerance for drone, and whether you live in a state where rust is a problem.
If you're after performance, you probably shouldn't make any changes. There's a great article floating around written by Bill Visnic for Edmunds, where he interviewed one of the original engineers who designed the 5.7 LX exhaust system for D-C. He explains in detail why it's such a great system, and the fact that it's still largely unchanged (except for a few muffler updates) tells you something about how well it works. I doubt you'll be able to improve performance with any aftermarket or modified exhaust.
If you're looking for improved sound, you've got a lot of options. One of the most popular is the "Brylcreem mod", AKA the "tuna boat mod", where you cut out your mufflers and replace them with straight pipes. On the plus side, this will give you a louder, throatier sound, it's cheap and easy, and you're not going to have to deal with hanger and fitment issues the way you would with either a resonator delete or an aftermarket catback. You can Google "charger muffler delete" and gauge for yourself whether or not most folks tend to be satisfied with this mod. There are a few downsides.
First, when you're researching, you'll discover that many people don't know the difference between a resonator and a muffler, so that they'll announce very authoritatively that they performed a muffler delete when it was, in fact, a resonator delete, and vice versa. Keep in mind that in any LX, the resonators do all the heavy lifting. That's why the result of a muffler delete is pretty predictable. For the most part, things just get louder. But a resonator delete is harder to do, since there are some pretty severe bends and hangers to deal with. When you create the new pipes, you usually have to settle for crush-bent, mild steel pipe that won't flow as well as the smooth, mandrel-bent stainless steel factory system, and it will start rusting on the drive home from the exhaust shop. A resonator delete will also result in unpleasant cabin drone, which you'll have to either learn to live with or do your best to mitigate by cobbling together other components like bottle mufflers or glasspacks.
Some people don't like the muffler delete sound. Luckily, you can find plenty of examples on YouTube and decide for yourself, just remember to use "Charger" in your search, there are considerably more of them out there.
Another issue with the muffler delete is the change in your exhaust velocity. You'll find a fair few online arguments about this issue, where someone will post (again, very authoritatively) that the Hemi "requires a certain amount of backpressure" and reducing it kills your performance, or some similar argument. I think the real issue is that altering your exhaust velocity so far upstream, where the gases are still very hot, causes your powerband to shift. I tend to believe that this concern is mostly overblown. I don't think there's any net power loss, because you're likely gaining it back on the upper end. But still, I feel that with a two-ton Charger or 300, I want every bit of low-end grunt I can get, and I'm not willing to lose any of it, so a muffler delete isn't for me. But you might be perfectly happy with it.
If you're looking to spend money..and it sounds as though you are...there are some good aftermarket systems out there. Corsa is one of the best, but they're crazy expensive, which I guess is good if you're looking to throw money at the car. In terms of bang for your buck, the
Solo Mach XH is hard to beat. It's the only aftermarket system I know of that includes adjustable J-pipes that preserve the anti-drone functions of your original resonators, so there's some engineering behind it, and compared to other high-end catbacks, it's a little more reasonably priced.
I originally intended to do a muffler delete on my '05 300C, so I bought two 4' lengths of stainless steel pipe. But I came across an all-stainless OBX/Maximizer CR12050CH catback for less than $300, so I decided to go that route. I'm very happy with it, it's definitely louder and throatier than stock, but it's more of a "Touring" exhaust, so if you want something really loud, it's probably not a good choice for you. Also, it's only marketed to fit 05-10 300s, so you would have to do a little work to get it installed on your car.
On my '14 Charger R/T Blacktop, I tried a mod from a user named drex on our sister site, Challengertalk, which he in turn lifted from a Corvette forum. Basically, you modify your resonators for a little more sound. It's perfect for my purposes...I just wanted it to sound like a Hemi and not a sewing machine, which is what the factory exhaust sounded like, to my ears. But that mod isn't sexy, because you don't get to spend a lot of money.
Hope this helps!