Solid wire - better electrical conductivity, but is easier to break the wires - use this to go through walls/attics/crawl-spaces
Stranded wire - slightly less conductivity, but is much more durable - us this to go from wallplate to device.
As bill001g said, be carefull of cheap cable on amazon/ebay. Those are often copper clad aluminum. Best price on all-copper cable in the usa/canada is from monoprice.com
Also, there is little to no benefit of cat6 cable.
Both Cat5e and Cat6 are capable of 1gbps for the full 100 meters (300 ft) of max distance.
Cat6 is technically not certified for 10 gbps, in a lab they can get up to 55m but no garantee.
Cat6a on the other hand can support 10gbps for the full 100m.
So in short if i you want 1gbps then just get Cat5e, if you want to 10 gbps capable for the future (probably still 10 years until practical for home use) , then use Cat6a.