The best way to stream is to have 2 pc-setup. Period. Streaming eats a lot of cpu power and there is no way you will have better stream quality with 1 pc than with 2pc setup. Unless you dont have a pc with 2 cpus inside which is quite exotic and expensive as hell i guess. And it's not for gaming.

 So you can buy avermedia live gamer portable lite  (around 150$) to save some bucks and you dont need any splitter. Just make sure that you can use avermedia's hdmi input (check you laptop video output). And you will probably need hdmi cable, if it is not going with the capture card. 
The difficulty about 2 pc setup is audio. but all you need is 2  3.5 mm cable splitters - one for your headphones and one for your mic. Mic goes into splitter and than to both pcs. Line out from laptop goes to splitter and than one goes to your headphones, another - to mac line in. So it's an additional 30$ For audio cables and splitters. With capture card you will fit in 200$ easily, if you dont have professional mic with xlr or usb output. Also there are some ways to send audio thru lan. 

Answer on top is ridiculous.    They say that lgp lite is too expensive (it's around 150$) and suggest you to buy a new pc, which is about 1000$. Wtf?

Good luck