Looks like you have 1 PCI-E x16 slot and 1-2 PCI slot internally.
If you have a separate graphics card then your PCI-E slot is arealy used so internally you could use a legacy PCI slot card (which will only go up to wireless-G MAYBEE 150mbps wireless-N.
If you are in same room as the router then use an ethernet cable which is ALWAYS better then wireless
If 1-2 rooms from router then get a USB wifi adapter
If more then 2 rooms from router then dont bother with wifi and get powerline network adapter.