Solid wire generally has better performance characteristics and should be used for all horizontal wiring. Stranded wire is less likely to break from movement and is excellent for patch cables. RJ45 plugs come in a stranded and solid wire version. Be sure to match the plug to the wire type. If you have to use the rectangular shaft for round cable glue the cable into the shaft with hot- melt glue.
Cable is available on both spools and in spool-less boxes.
It's a matter of personal preference as to whether you buy spooled or spool-less cable. The spool-less box doesn't require a spool stand and is considered easier for one person to handle. The spool-less cable might be slightly more expensive. 568A Category 5 Cable 1. A conduit or UL approved cable tray is acceptable for supporting the cable.