Should I choose Cat5e or Cat6 installation cable?

Cat5e is entirely capable of Gigabit Ethernet and is still a perfectly serviceable choice where that is the requirement. Cat6 gives you more transmission headroom, is specified to 250MHz rather than 100MHz, and is the more natural choice for a new installation where the small extra cost is acceptable.

Cat6 does not make a 1Gbps Ethernet link run faster than 1Gbps; what you are buying is a higher cabling category and more margin, not a secret second accelerator pedal.