Welcome, Newcomer. A heatsink is the metal object placed over your CPU for heat dissipation. The fan that goes on top of the heatsink is there to pull the hot air away from the heatsink. You do need this, and if you get a "Boxed" CPU, you'll get the stock heatsink and fan.
The Radeon HD 4650 comes with it's own heatsink and fan.
As the person above said, yes, a heatsink is absolutely needed, always.
For you, you would want the get the second one as it is slightly faster and includes a stock heatsink and fan as well. If you are planning on overclocking in the future, you would want to buy a better heatsink than what is included. However, for your needs, you will be fine with the stock heatsink.
You seem to imply in your question that you are asking what heatsink you should get for the video card (4650) as well. Video cards will always come with their preferred cooling method already attached for you, whether it be a small fan, a giant heatsink/fan combo, or just a passive heatsink. You do not need to worry about attaching cooling to your video card.
The 2nd processor has a higher stock speed. If you aren't planning on overclocking, you should get the 2nd processor.
If you get the first processor, you will need to get an aftermarket heatsink, which start as low as $5-6, but can run much higher for premium parts. Tom's just did a round-up of budget coolers, and there are certainly more available out there.
This processor is probably the best buy, as it's $1 less than your 2nd listed processor, but it's .1 GHz faster and comes with a heatsink.