good specs/internet are not so vital (there is an extremely low bare minimum though). it's possible to have a decent-looking stream with crappy hardware and crappy upspeed, but the crappier your conditions the more effort/creativity you need to configure everything just right. anyway, basically every capture device will encode the video itself before your pc will ever see it, so your pc doesn't really need to do a lot of work; it just needs to be able to run the streaming software and handle encoding the final video that everyone else sees. use:
xsplit (easier to use),
obs (more resource-efficient).
for reference my upspeed is 0.6 mb/s (extremely bad) but I make up for it with an i7. other aspects of hardware are not nearly as important as the processor, although i'm guessing simply having a graphics card at all will broaden your options quite a bit. obviously the greater your upload speed the less efficiently your pc will need to encode to get it to look nice. it's fairly common for most to stream somewhere between 1-2 mb/s (their actual upspeeds are usually in the 3-5 mb/s range; it helps stability to stream significantly under your max). I personally stream at 450 kb/s, still very nice-looking considering.
I'm guessing you want to stream skyward sword-related stuff? keep in mind that even via component the wii will only output at max 720x480 video, so there's no need to buy anything fancy in the way of capture devices, anything made for standard def will do. buy: ezcap (cheap/great value), dazzle (slightly better quality), also anything in kmart/bigw/whatev labeled as a dvd maker or vhs digitizer or similar are basically just capture devices bundled with (usually ****ty) dvd authoring programs.
cost-wise? anywhere from $5-$50 for the capture device. you almost definitely do not need to upgrade your pc/internet but if you choose to do so then you will need to do your own research.
i think that covers the basics. i can help later with setting everything up once you get it all going if you have questions about programs/codecs/drivers and whatnot.
