Most any CPU should do fine with blu-ray playback and the integrated graphics are enough to have smooth playback. You might want to check on CPU benchmarks for ripping Blu-Ray, I have a hunch Intel might be the better option here.
One thing to note, you need a retail Blu-Ray writer because those versions come with the necessary software to actually play Blu-Rays.
I went for a low power Intel build:
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: Intel Core i3-4130T 2.9GHz Dual-Core Processor ($134.49 @ Staples)
Motherboard: Gigabyte GA-H87M-D3H Micro ATX LGA1150 Motherboard ($98.97 @ OutletPC)
Memory: G.Skill Sniper Low Voltage Series 8GB (2 x 4GB) DDR3-1600 Memory ($80.17 @ NCIX US)
Storage: Kingston HyperX 3K 120GB 2.5" Solid State Disk ($89.99 @ SuperBiiz)
Storage: Western Digital Caviar Green 3TB 3.5" 5400RPM Internal Hard Drive ($109.99 @ Newegg)
Case: Silverstone ML04B HTPC Case ($74.99 @ Amazon)
Power Supply: Antec EarthWatts Green 380W 80+ Bronze Certified ATX Power Supply ($47.98 @ OutletPC)
Optical Drive: Asus BW-16D1HT Blu-Ray/DVD/CD Writer ($82.79 @ NCIX US)
Total: $719.37
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-01-03 07:42 EST-0500)
This gives you 4 threads for ripping, at a third of the TDP. A bigger storage drive because Blu-Rays will fill that 1TB drive up in no time. I also added an SSD for your OS and apps, this will greatly increase your performance and in my opinion is a must in computers these days.
For a capture card, this is the kind of thing you need:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
However it only does 1080i, you may need to hunt around for something that can do 1080P.