Help with Xbox live question- Not sure if i should get it?

If im going to get xbox live im going to need to buy:

Xbox360 wireless network adaptor= £60/$120

Microsoft 12 month gold subscription= £40/$80

and a wireless router= £60?/ $120

basically im not sure if ill be able to go on xbox live because my internet when i did speedtest was download 1889 and upload 376 so if it wont work because its too slow i will have wasted nearly £200/$400 on nothing.

Also Do I get a wireless router or a wireless modem router and i dont know which one to get becuas ei want one which will work with my xbox 360 obviously and my room is the other side of the house to the pc and its upstairs.

I would rather get one from Argos (UK) so if anyone in the uk knows stuff about wireless routers can you search the argos website for me and tell me which one to get thanks.

http://www.argos.co.uk/static/Browse/catalogId/1500000701/identifier/8963200/jspStoreDir/argos/Trail/C%24cip%3D1500006463%3EC%24cip%3D1500006471.htm

whats the diffrence between a wireless router and a wireless modem router and how do i know which I need to get?

Also I cant have a cable because there at opposite ends of the house.