Hello, and welcome.
The ASUS 7970 shouldn't have any problems connecting to the 3D TV, and using the AMD HD3D Technology you should also be able to benefit from the 3D availability. However you will need a high quality HDMI cable, or use a Dual Link DVI cable. AMD HD3D Technology
On-board sound is actually pretty good now, a motherboard is no longer just connecting everything it contains WiFi, sound and some extra processing and overclock ability's. If you have room in your budget for a sound card, you will get better results. (The Creative Sound Blaster Is Really good and comes with mic too)
Generally 'Gaming Speaker' mean 'Crap Speakers', company's hope by rating the gaming it gets them sales no matter what quality. When choosing speakers don't restrict your self on type; Sound Bars, 5.1 systems, Gaming speakers do the research. Personally i ended up going with the Corsair SP2500 and they are of unbeatable sound, however as your using a TV, i would look for some speakers with an optical input, so everything that plays through the TV can output into the speakers.
Most sound systems will have a AUX (3.5mm headphone socket) or RCA/Phono (Red and White) or and Optical input, there is always A way to connect multiple devices up to one set.
Intel Core i5 2500K /-\ 32Gb 1600mhz RAM /-\ Asus P8Z68/GEN 3
2x 256Gb Crucial M4 /-\ Crossfire XFX HD Radeon 7950 Black DD
Sound blaster Z /-\ yourpcperfect.com /-\ Windows 7 Pro