Is your $16k budget including predicted costs of maintenance? If you're looking at a premium brand like Cadillac, you're looking at something with higher miles which = maintenance costs early on. With that budget, I'd look at something on a used or Certified Pre-Owned lot that has few miles and is only 2-3 years old, since as a recent graduate you don't have as much of a cushion should something catastrophic go wrong.
Think about this car purchase not as something that you want now, but something that you want in 3 years. If you buy an early model CTS now, its going to have lots of miles. In several years, what will that car be to you?
Will it still have the appeal it has today?
Will it be worth $16k? Will it even be worth $10k, since it'll certainly be over 100k miles? How much money are you going to have to sink into it after the initial purchase?
How much do parts cost on a 6-7 year old premium car as opposed to a 2-3 year old midrange car?
For instance, we've got an '09 Ford Taurus Limited in our Certified Pre-Owned inventory. I will not post price to try to keep this from being a pimping thread, but mods edit this if necessary; I just wanna give some perspective on other cars that are out there. This car is a short way out of your price range but has a lot of very nice features that compare to a $16k CTS, but in 3 years this car will still be under Certified warranty (unless you drive 20k+ miles/yr). That means you're going to have to spend minimal money beyond the initial purchase. I'm not at all suggesting that this is the car for you, but the point is that there ARE very nice vehicles out there within your price range that will give you a whole lot more reliability and will GUARANTEE that you spend less in the long run.