These are two great questions and the exact same questions I had before making my purchasing decision. So I did some research and here's what I found:
Shielding is really only necessary if you are around heavy electromagnetic interference, like power generators, magnetic resonance imaging scanners (MRI machines), and maybe a lot of high tension power lines. The disadvantage to shielded cable is that you're probably not going to be able to run them through your walls without removing some drywall. The shielding is not really flexible enough to run through a fire break and then do the 90 degree bend to come out of a small hole at the base of the wall.
CAT5 vs CAT6 is almost a no-brainer. CAT5 is probably fine for all current applications but as technology improves, applications are requiring more and more bandwidth. If you want your cable to keep up with the increased demands of technology, you will want to go with the highest bandwidth supported, which means CAT6. If your bandwidth needs are limited and you're just trying to wire up a device because it doesn't support WiFi, CAT5 is fine. The reason I say it's a no-brainer, however, is that Best Buy sells the Insignia 50' CAT6 cable for $34.99 and the CAT5 cable for $29.99. Five bucks is a small price to pay to future proof your Ethernet.