My internet provider, which is Cox Cable has a "faster" service available would this translate into better online speed and maybe less lag when playing PS3?

When you get into broadband internet, the real bottleneck for gaming in my opinion is the upload speed (the lower of the two numbers they give on your package). For example, if they offer a 3MB/384kB package and a 5MB/768kB package, the real place you'll see improvements would be due to the upload speed of 768K. As far as which package would truly be needed to have a good online gaming experience, I don't know. I have a 5MB/512kB package and I have not experienced any lag on my 360.

If you are having lag issues with your current package, going to the faster one may help, but you want to find out the difference in upload speed. Playing an online game is a two way street.

Yes, you need to find out the download and upload speeds of each package. I went back down to a 6MB down/384kb up from an 8MB down/768kb up Comcast package, and I noticed no difference on PC games or 360.