Here's how I shop, I try to find the "sweet spot" where I get a lot of bang for the buck, and enough power so I don't have to worry about changing anything for a few years.
I start off with this for an overview:
http://www.tomshardware.com/reviews/gaming-graphics-card-review,3107.html especially the Hierarchy chart at the end. (Always look to see if there's a later one, it gets updated every couple months). This gives me a starting point of a few cards to investigate in more detail - for those, I look up benchmarks on the games I care about and current/likely sale prices.
Once I narrow it down to a couple, I google for problems with the games I am planning to run, and read any discussion about sufficient performance, incompatibilities, etc. Make sure it's fairly recent, a lot of problems are solved by new drivers or game updates - if you see discussion of problems look for later mentions that it's solved. Also get familiar with brand and model differences in cards - potentially different clock speeds, memory, cooling, etc from the "reference" model. Read reviews, read benchmarks, look for direct comparisons discussions.
Now if you really want to save money and can be a little patient waiting for a deal, start haunting the sales - a couple times a day, check for the hottest sales on deal sites like
http://www.pricewatch.com/video_cards/http://www.fatwallet.com/video-card-deals/ and
http://www.fatwallet.com/forums/hot-deals/computer/http://slickdeals.net/forums/forumdisplay.php?daysprune=7&vote=0&intagid%5B%5D=9&f=9&sort=lastpost&order=desc (I'm not sure the above will work - go to their "hot deals" forum, filter on the left to Include Computers and then Apply. Alas you can't just pick "parts->video cards" because quite a few guys who post the deals don't set the categories that low so you'd potentially miss some hot deals)
http://hardforum.com/forumdisplay.php?f=28http://www.techbargains.com/catsearch.cfm/0_2_5Sign up for newegg's deal newsletter to get promo codes for their sales:
http://promotions.newegg.com/neemail/latest/index-landing.aspx?cm_sp=emailsub-_-homepage-_-promoIf you live in a city near a Microcenter, check their site periodically/sign up for their emails. They are better on cpu/mobo sales than video cards, but once in a while they have decent deals on other stuff.
Keep looking on Google Shopping for the various models you're looking for (but BEWARE buying from some dodgy shop - I'll pay a few bucks more to buy from Amazon, a few less bucks more for the 2nd but still pretty reliable tier of newegg, Tiger Direct, superbiiz and directron).
I have only been looking at AMD cards recently because I wanted something I can do bitcoin/litecoin mining on - (your parents might not go for that though, you have to leave the PC on all the time and it uses a pretty sizeable amount of power).
So from my research, for around $200 one of the newer 7870s is pretty good bang - especially the new 7870 LE looks really solid. For the tiny price increase over the old 7870s a 7870 XT or 7870 LE would be the way to go, if you could find a good sale (don't see anything TOO exciting currently, although this one for $220AR isn't too bad:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814131487 )
For just over $250 AR you could get a 7950 which is a little step up but also has another 1G ram (that you def. don't NEED if you're running at 1080) - newegg has this one for $258 AR (if you use the promo code off the newsletter as mentioned above)
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150590 or Tiger Direct has this one for $269.99AR
http://www.tigerdirect.com/applications/searchtools/item-details.asp?EdpNo=8078201I got a 7970, it was about $330AR at the time (SMOKING deal around Black Friday) and so far spend far more time playing roguelikes on it - I haven't even loaded the free games it came with :p