The best would be to run the cable inside a plastic conduit. The conduit will protect the cable from the elements and also aid you in replacement or installation of additional cables. The choice of CAT5 or 6 is based on what you need. Both cables can use the same connectors. The difference would be the speed that can be transferred on each cable. CAT5 is 100mbps, CAT5e is 1000mbps, CAT6 is 1000mbps, CAT6e is 10000mbps.
There are several types of each cable. UTP is unshielded so it's just the wires inside a plastic coating, FTP is foiled so its the wires covered with a thin plastic sheathe and then a thin foil sheathe and then the plastic outer coating, STP is shielded so it has a protective sheathe over or under the plastic coating, SFTP is shielded and foiled so it has the foil sheathe around the wires and then the protective sheathe over or under the plastic coating.
The foil aids in the reduction of electro-magnetic interference. The shield protects from potential damage caused by the elements, objects falling on the cable and so on.
Each variant has a price and the more protection you go for, the more expensive.
If the cable is running next to a power cable, then its better to get FTP cable. If it's running on its own, then UTP is fine. The other thing to consider is, the cheaper the cable the more of a chance it will be copper coated aluminium wire. The pricier the cable, more more of a chance it'll be solid copper wire. Solid copper wires provides better signal transfers and can allow for longer cable runs. Normally the writing on the cable specifies what kind of wire is inside. It'll probably say, CAT5e UTP SOLID with a bunch of numbers. That means the cable is Category 5e, Unshielded Twisted Pairs of wire made of Solid copper.
Hope this helps.