The savage is a solid, accurate rifle with a lot to recommend it. The savage action is a 'push feed' like the Remington 700. Unlike the Remington the barrel attaches to the action by means of a large nut (the Rem barrel screws into the action). This nut is a unique feature and makes Savage rifles easy to recognize. It also makes switching barrels relatively simple, and many Savage owners switch between multiple chamberings on the same action.
Savage rifles produced in the last 5-6 years or so have an extremely good reputation for accuracy, and are consistently among the best values in the rifle market. If you're not anxious to spend lots of money and accuracy is important to you, then Savage is hard to beat.
There are a few downsides.
Many people find Savage rifles ugly. The barrel nut and the SAVAGE logo etched on the bolt body are frequent targets for this criticism. If you're someone who likes to admire his rifles as objects d'art, then perhaps a Savage is not for you. If you like to shoot your rifles and admire tiny groups and dead animals instead, then you may safely ignore this criticism.
A related complaint is often leveled at fit and finish, and sometimes materials. Savage plastic stocks are of remarkably poor quality, even in comparison to the already-low standards for plastic factory stocks. Their wood stocks have improved in the last few years, but still lag way behind Remington, Sako, and Browning. In addition, trigger guards and other accessory parts (safeties, etc.) are usually made of cheap materials and are often indifferently fitted. Again, these criticisms may or may not be important to you. They don't have a thing to do with how well these rifles shoot.
Savage rifles don't hold their value well. Don't expect to get your money back if/when you go to sell one. For this reason I'd actually argue against getting the 14/114 Classic. They're 'nicer' rifles, which to me means that you're paying extra for features that the used market will ignore or at least heavily undervalue. A bit like getting custom wood panelling installed on a Pinto--it sure costs more, but it doesn't mean you can sell it for more.
If I were in the market for a cheap, reliable, accurate hunting rifle, I'd look at the Savage 11/111G, but I'd also have a hard look at the Tikka T3 and the Remington 700 SPS. Both of these rifles have equally good reputations for accuracy and reliability, and they both offer different options in terms of ergonomics (how well does the stock fit you?), fit and finish, and chamberings.