Assuming that the beta requirements are similar to the final game's ones:
http://us.blizzard.com/support/article.xml?locale=en_US&articleId=26242
http://www.legionhardware.com/articles_pages/starcraft_ii_wings_of_liberty_beta_performance,4.html
Then you'll be able to spend a lot less than $1100 and play it fine. More like $700. If you buy separate components and put it together yourself or get a local PC shop to do it.
CPU: In the price range, AMD. The game can use four cores, so an AMD Athlon II X4 635 (4x3.0GHz) should be more than enough.
GPU: Since Nvidia has no effective competition, AMD. HD 5750 or 5770, unless your resolution is higher than 1920x1200.
Motherboard: For an AMD CPU I would use an AMD motherboard. You could go Nvidia but they're a little outdated.
CPU, $100: http://www.newegg.com/Product/Product.aspx?Item=N82E16819103702
GPU, $130: http://www.newegg.com/Product/Product.aspx?Item=N82E16814150448
RAM, $100: 4GB DDR3-1333, any brand
Case/PSU: ~500W, $60 total
Motherboard, $80, e.g. AMD 785G (AM3): http://www.newegg.com/Product/Product.aspx?Item=N82E16813130247
Hard Drive: 1TB, ~$80
Operating System: Either transfer your current one, or 7's about $100.
Total: $650
If you really have no use for the extra cash, and you want to play much more demanding games than Starcraft II:
CPU/Motherboard: Intel, unless you want 6 cores
GPU: Still AMD, unless you think a GTX 465 is good value.
CPU, $200: http://www.newegg.com/Product/Product.aspx?Item=N82E16819115215
GPU, $290: http://www.newegg.com/Product/Product.aspx?Item=N82E16814161330
RAM, $100: 4GB DDR3-1333, any brand
Case/PSU: ~600W, $70 total
Motherboard, $130, P55: http://www.newegg.com/Product/Product.aspx?Item=N82E16813130248
Hard Drive: 1TB, ~$80
Operating System: Either transfer your current one, or 7's about $100.
Total: $970