As it's been said a hundred times before, all-grain is cheaper in the long run but requires a lot more up front equipment cost.
You'll need a mash-tun, of course, and there is a great post here on making one out of a beverage cooler. For your pickup you can use a toilet line screen like in the post, make a manifold like this one
, though they are a bit easier to make for rectangular coolers than round beverage ones, or make a false bottom like the one I did here
that I've had great success with.
From there you can do batch sparging or fly sparging, though with fly sparging you'll need a hot liquor tank (usually just another cooler), valve and something to distribute the water evenly across the surface like a sparge arm or colander.
You'll also need to get at least an 8-10 gallon stock pot/boil kettle to collect wort. I use a 10 gallon food-safe aluminum one I got from Amazon that I've had no issues with. Also a high BTU propane cooker (Like this one
) if you've been using a stove since home stoves usually don't get hot enough to boil 7+ gallons of wort.
But most importantly you'll need a lot of information and Palmer's All Grain Brewing section of How to Brew
is the best place to start.
I'd start off with a simple recipe like an Amber Ale or something just to get used to the process. All Grain introduces a ton of new variables and processes, so adopting the KISS philosophy will benefit you greatly while starting out.