I need help to build wireless home network

I have a DELL notebook, an old desktop, smart phones and broadband connection. I want to buy two router preferably TP-Link since the brand is comparably cheap and most available here.

I want to buy TP-Link TL-MR3420 (http://www.tp-link.com/en/products/details/?model=TL-MR3420) as main base router to share internet connection(The broadband Ethernet cable goes in WAN port). My notebook will connect to this wireless connection.

In another room(8-10 meter far having two 5inch brick wall in between) their is an old desktop computer which DOES NOT have any wireless adapter. So I think I can buy a wireless adapter like (http://www.tp-link.com/en/products/details/?categoryid=243&model=TL-WN722N). but I'm guessing if I buy a router like (http://www.tp-link.com/en/products/details/?model=TL-WR720N) which will be connected to desktop using Ethernet cable could give me better reception with approx. same price. Is it possible that this router can receive/connect the base router network Wirelessly and desktop could get internet connection without wireless adapter?

You could suggest any other router preferably TP-Link. Can I get full speed as subscribed from ISP in receiver router if other devices are not connected? Thank you.