I am gradually acquiring my upgrade equipment to start all grain brewing. I was a good boy this year and Santa brought me a 10 gallon Igloo drink cooler that I am going to use for my mash tun. I am debating between buying a false bottom or a kettle screen. I like the economic solution of a kettle screen. But, will a false bottom be a better option and worth the extra money? What pros and cons does everyone have regarding each of these set ups?

I use a copper manifold I built for very cheap, and I get pretty good efficiency. My cooler, however, is rectangular which made that option more practical.

IMO, if you have the funds, go with a false bottom. My belief (no experience), is that a full false bottom will help avoid "channels" in your sparge that might be created with a kettle screen. On the other hand, the difference in efficiency is probably nominal at a home-brew level.

Actually, as far as a manifold goes, I guess you could do it in a round cooler. Jim Palmer's "Hot to Brew" has a great little section on it. It's a great way to go since it's cheap and effective. Here's a Link: http://www.howtobrew.com/appendices/appendixD-1.html .

BEWARE THE COOLER TUN FALSE BOTTOMMMMMMMMM!

Seriously, though. I've seen a few posts of folks who have problems with false bottoms in a cooler tun. It seems the holes in the false bottom are too large, and allow grain particles through, which clog their drain valves. The simple solution is to cover the false bottom with a bit of stainless screen.
Efficiency-wise, I would have to agree that the false bottom is probably the better option. But I always say that good efficiency does not make better beer! Just cheaper beer. And on a homebrew scale, the difference between 70 and 75 percent efficiency is just not enough to worry about, IMO.
For my first tun, I used a cheap-o screen which I pulled off of a (brand new!!!) water line for a toilet. Now, I can't stress enough that the NEWness of this water line is paramount! I used that tun for a few years, and I had efficiencies ranging from 55 percent to 78 percent. My efficiency rose tremendously when I started using a higher quality grain. Nothing different in the process, just a higher quality imported grain.
Whatever you choose, I'm sure it'll work just fine. I wouldn't stress over the option too much.

Take it easy!

+1 on everything, Guitarlord! We must always remember the mantra: "Relax, don't worry, and have a home-brew." Do what works for you and, remember, all the options will work. That's why there's debate between them.

Muchas gracias amigos! I think I am going to opt for the false bottom. I found a pretty reasonable price with Northern Brewer.