A PCI TV card can be as little as £30 or under.
I would presume that running a co-axial cable from your Freeview set top box to the co-axial plug on the TV card should work.
Of course the set top box will require a TV aerial signal. Getting one to it and also to retain one for your second set top box box can be done using a two co-axial output TV signal amplifier; this should cost under £15-£20.
You shouldn't need to upgrade your specification in any way re graphics cards.