300 ohm twinlead to Coax?

You should have clicked the little "accessories" icon on that same Radio Shack page.....you need the "Matching Transformer" (which hooks to the antenna itself), and coaxial cable (to go from the transformer, all the way to the TV).

If there's already flat lead (300-ohm twinlead), just replace it. Twinlead is too much trouble to mess with any more, although it CAN be a little bit less loss....if you put it in exactly the right way.

Yes, connect the balun (transformer) at the antenna terminals (where the flat wire is connected) and just screw on the coax.

Be sure and buy RG6, not the cheaper, but similar looking RG59 sometimes sold at big box or discount stores. Look on the packaging or on the info stamped into the side of the coax. RG6 has less loss than RG59.

Any TV antenna will work for you, if it is suitable for your distance from the towers and the channel bands/frequencies being used in your area. There's no such thing as a "digital" or "HDTV" antenna. That's just marketing BS to confuse the buyer into thinking they need something new to get DTV.

If you don't feel like re-running the twin lead, and if the twin lead is already at the TV, you might want to try this:

http://www.radioshack.com/product/in...ductId=2062054

Connect the twin lead to this transformer, and just plug the transformer in the back of the TV's antenna input.

If you need to extend the twin lead, then you also need an f-coupler, or barrel splice like this to extend the rest of the way from the transformer to the TV with coax.
http://www.radioshack.com/product/in...ductId=2103648

This is just a suggestion, as you might be fine with what you have. But this is assuming the twin lead is in good shape and not cut anywhere. Otherwise as others have suggested, running new RG6 is recommended.
Save your receipts from Radio Shack in case something does not work.