Yep, Rocksmith transforms your console into a mini integrated amplifier during gameplay. You would still need an amp if you wanna play the guitar without the game though.
Rocksmith is an excellent instructional tool for almost all levels of guitaring. Even has basslines for those interested to learn bass guitar as well. However, I personally feel the gameplay is not as intuitive as it should be. It is geared more towards the Guitar Hero style of articulation. So if you are familiar with Guitar Hero, you should do fine. I however, SUCK at Guitar Hero and thus Rocksmith is kinda undecipherable to me! Much more comfortable with traditional guitar tabs.
Another game out there called BandFuse uses this more traditional format, I find it much easier to understand though I haven't actually tried it myself. Here's a vid of the gameplay with a simple song:
Having said that, learning guitar through these games exposes you to the danger of using the wrong technique to play. For example, they do teach stuff like picking technique but do not correct your technique during gameplay. So unknowingly, you may be getting it wrong, which means having to unlearn the wrong technique and starting from scratch again.
As for which guitar to get, I suppose something versatile and comfortable to play should be your choice. Personally, I wouldn't jump at the cheapest guitar out there. Instead, try a few within your budget to see which suits you the best it terms of comfort and feel. Most of the time, this has to do with the neck profile and body shape. Usually, the right guitar will have a conversation with you, it lets you know that it's the ONE for you. I know this sounds like a lot of hocus-pocus BS, but somehow, it works for me! Generally, Stratocaster and Superstrat-shaped guitars have a universal appeal. You may want to try the likes of the RG-series Ibanez, traditional Fender/Squire Stratocasters, Charvel DX-1, Schecters etc...