While I can't comment on exactly how well any of these will run WoW or Civ V at 1920x1080, the options I saw worth mentioning for less than $50 on Newegg or Amazon were limited to nVidia 520s, 610s and 620s, and Radeon 6450s and a 6570.
Here are the specific cards I found, ordered by price.
ZOTAC ZT-60602-10L GeForce GT 610 for $9.99
MSI R6450-MD1GD3/LP Radeon HD 6450 for $14.99
Galaxy 52GGS4HX9DTX GeForce GT 520 (Fermi) for $29.99
ZOTAC ZT-60502-10L GeForce GT 620 for $29.99
XFX HD-657X-ZDF2 Radeon HD 6570 for $39.99
I did not include Radeon 5450s or nVidia 8400s and 210s as they did not cost any less and would give worse performance. Here are the cards ranks (best to worst) according to placement in the
TH Graphics Card Hierarchy Chart:
Radeon 6570
Radeon 6450
[Integrated: Intel HD Graphics 4000 falls here right between these two, so that should give you an idea where your integrated graphics fall]
nVidia 520
nVidia 620 (not ranked)
nVidia 610 (not ranked)
Although the 620 and 610 are not ranked, looking at their technical specifications (CUDA Cores, Core Clock, Memory Bandwidth, Memory clock, etc.) in comparison to the nVidia 520, I would expect the 620 to be roughly on par with the Radeon 6450 and the nVidia 610 to match performance of the 520 (their specs are completely identical).
I hope, even though I can't speak specifically as to how well any of these will run WoW or Civ V at 1920x1080, that this information helps. My guess would be that either one of the Radeon 6000 series cards should be able to get you through until you are ready to buy a "real" gaming GPU.