Which LCD Model #/Manufacturer?

I am going to replace the LCD Screen on my newly acquired MacBook Unibody A1278. It is a 2.0 Ghz Processor. unlike the video guide I found, it has the battery door. Is there a specific LCD that I need to get? I have found several sites claiming to have the correct one, but I am worried about them having the specific cable connector.

LP133WX2-TLC1 seems to be the correct part #. Any advice or help would be nice, as I am a very poor traveling musician, and this is something I *need* to get working as cheaply as possible. Also, will a hairdryer be sufficient in heating the adhesive, or will I need a heat gun as the tutorial states?

Thank you.

B