Does a motherboard with a PCI-E 2.2 work with a graphics card that needs PCI-E 2

Hi, im planing on upgrading my old computer on a low budget (for a gaming pc) so it can play modern games for a few more years.

I was on the pc world website at pcworld.co.uk and was looking at a new graphics card(ASUS ATI Radeon HD 5770 CuCore PCI-E Graphics Card - 1GB)which needs a (PCI-E 2.1 x16 bus interface) and i was also looking at the motherboard (ASUS M4A78T-E 790GX ATX Motherboard - AM3 socket) which has a PCI-E.

Are these components compatible with each other?

Also do you think the (AMD Phenom II X4 955 Black Edition Processor) which is also on the website with a 4GB DDR3 RAM be a good combination for the money which is excluding the RAM a total of £394.
(cant tell you what RAM right now because pc world stupidly doesnt sell DDR3 memory although it is on the website but you can't buy it from the shop or online)

Thanks for your time