no. cat 6 is for data beyond gigabit, you do not need cat 6. Its really only useful for people setting up a wired permanent home network who need to seek heavily futureproofed solutions. At this time gigabit is still taking off, and cat 5e handles it like a champ. Save your money, get cat 5e (pretty much everything is cat 5e even if it doesnt say so). For your cables you're good with stranded, in fact i'd say only get stranded cat 5e because you'll need flexible cables, solid core can hold a signal for a longer distance but will break if bent repeatedly.
-stranded cat 5e
-switch hooked up to router if you want net access, or you can just plug the modem straight up to the switch(way easier just to plug into router.
-dont worry about crossover or particular type, all newish switches/hubs/routers dont care
-as for food, zesty doritos, pizza(or the pop variety), and mountain dew (heck even coke)
Read the next part if you want to know what the difference between a router switch and hub in laymans terms.
rememebr, router's are specialized switches with the ability to communicate using the ip. Switches move data from one place to another using address's, hubs do the same but the data is sent to each port, its like a copier, hubs arent smart by any means, they pretty much just broadcast data, as opposed to a switches ability to select or switch where the data stream goes. This is why routers have switches, and why you need an ip, because without it the switch in the router it woudlnt know where to send the packets it recieved from the computer behind the ip its connected to. I know its not related, but you might want to know what the hell the difference is between them.
if some IT guy wants to correct me please let me know and i'll fix it, afaik this is correct.