Yes the port on the back of the motherboard is for ethernet, althought ethernet doesn't just include the RJ-45 port that you are refering to. LAN just stands for Local Area Network which they usually call the RJ-45 port on the back of the computer. It should work fine with a standard Cat-5 cable. You don't need wireless unless you have an Access Point inside of your house.
Firewire isn't used a lot unless you have an external drive or some models of cameras. So one port should be sufficient. In my opinion don't go for the card...
Hope this helped
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