Can a performance style network card be better then on-board lan? Can a home network "lag" your internet connection? How can I tell if I am getting optimal connections within my home network, and outgoing internet connection?

Well unless you have really fast internet your network card won't matter unless it's wireless. All modern computers have 100 mps lan cards and your internet is maybe 10 mbps. If you bought a computer in the last couple years you might even have a gigabit card. Now if your really interested you can benchmark your internal network by using qtest to check the speed between computers. As for checking if your using your internet optimally it's kind of hard benchmark. You can run all kinds of test to see your download and upload rates but there is no bechmark to tell if your using it optimally that I know of and I really don't know how you could not use it optimally. If you don't like your speed pay for faster internet but remember you can't get any faster than the web or file server your communicating with.

All current computers have at least one gigabit ethernet card, sometimes two. Many onboard cards still don't do TCP offloading, which means packets have to be processed by the CPU. But this only becomes an issue for servers which receive lots of traffic and need the CPU for other tasks. A home user will not notice any difference, so using the onboard NIC should be no problem.

There is also a NIC that does UDP offloading, which is useful for gaming. But this only processes UDP in hardware and queues UDP on the card with priority. You'll get better gaming performance buying a router that prioritizes UDP packets (that you can specify) as this will do it both on your network as well as towards the ISP. Note that this only affects the first hop, once the ISP recieves that packet it will eb queued the same as any other packets.

Using both will work cumulatively, but you're unlikely to see more than a 2-3 ms improvement unless you fill up your internet link with downloads, at which point the queueing will be noticeable, but most of this will come from a router with queing capabilities.

Buying only a NIC with TCP or UDP offloading will, for home use, not be noticeable unless you have a fully loaded single-core CPU and/or a saturated LAN.