What satellite dish do I need to purchase for camping?

Your best bet would be to just carry the standard receiver.  They are much easier to set up.  A kit like THIS > http://installeroasis.com/directv-satellite-dish-tripod-kit-c-42-p-1-pr-36.html would work fine.  www.dishpointer.com would help you find the general location to point the dish for your location.

What about this dish http://installeroasis.com/directv-oval-18x20-in-triple-lnbf-satellite-dish-tripod-kit-c-43-p-1-pr-54.html since it claims to get more local channels? Just thinking about some football games that are on local stations.

That kit is for HD, but you would not get all HD channels. If you want HD you need to go with one like this.

http://www.satpro.tv/rvportablesatellitedishkitfordirectvkitwithfoldingtripod-1.aspx

The Triple LNB dish gets the 110 and 119 satellites in addition to the 101 that the round dish receives.  There are no channels on 110 and the local broadcasts from the 119 are very limited.  If you go very far from home you won't get your local channels with any dish because to leave the footprint of the "spot beam".

This triple is a bit more difficult to align, but the procedure can be learned.

This is not advertised as an HD dish, in fact it says it does not get HD channels.

So there is no advantage in purchasing this particular dish as compared to the round 18" dish?

You are talking about this dish.

http://installeroasis.com/directv-oval-18x20-in-triple-lnbf-satellite-dish-tripod-kit-c-43-p-1-pr-54.html

Because this one will get all your HD Channels...

http://www.satpro.tv/rvportablesatellitedishkitfordirectvkitwithfoldingtripod-1.aspx

I was not necessarily trying to get the HD channels. I am trying to find out which satellite is best for  camping and that is compatible with my directv receiver.

Stick with the round 18" dish.  It's smaller and easier to setup.  

This infofrom http://installeroasis.com/directv-oval-18x20-in-triple-lnbf-satellite-dish-tripod-kit-c-43-p-1-pr-54.html  is what has me confused.

A key question is how far away is your camp area?  If you want the New Orleans locals you'll need the 3-LNB Phase Dish to receive 119º satellite.

We usually go camping within a two hour radius of home but do occasionally go to Arkansas or Mississippi. I would like to catch local channels if I could. So would the 3-LNB Phase be the answer or not really?

As long as you're located within the spot beam coverage of the New Orleans locals (are those your current local stations?), then you'll want the 3-LNB Phase III dish.  That radius is probably a couple hundred miles, but can vary considerably.  Outside of that coverage you won't receive the New Orleans local stations.  

You have to switch to a multi switch on your box. Go to satalite in the menu and switch it to multi switch. you must switch it before you set the dish type!