SSgt Falso,
None of the KGs, i.e. 250s or 175As, etc.. do not support routing protocols on the PT or CT side.
So, you would need to run static routes on your switches and routers. That is not an issue since you have very few devices on your network.
As for Qos, here is good document to start with. When deploying Qos, you have to make sure you deploy it end-to-end.
http://www.cisco.com/en/US/docs/solutions/Enterprise/WAN_and_MAN/QoS_SRND/QoSDesign.html
As far as spanning three, I do not see a physical loop in your network. so spanning tree does not play a big role here.. You can run rapid-pvst in the background in case there is any need for it. Make the L3-3560 the root bridge since it is in the center of your network. Good idea to run portfast on your access ports only.
Also, here is document on root guard
http://www.cisco.com/en/US/tech/tk389/tk621/technologies_tech_note09186a00800ae96b.shtml
HTH
