If it's like the 'burban the connector for the trailer brake is in the black box behind and left of the brake pedal, and you'll need one of these to wire it in:
Valley Part No. 30408 - Standard Electronic Trailer Brake Control Wiring Harness Trailer Brake Control Connectors
That link is from googling "trailer brake harness yukon avalanche", to set you in the right direction.
Here is a page showing the black box I'm talking about:
How to install an aftermarket Brake controller on 1999-2006 GM Trucks
The "expensive shocks" is if it has the Autoride option, at least that's what my Yukon calls it. They are active shocks that electronically adjust damping based on road condition, tow haul mode, steering wheel sensor, etc. Not sure if the avalanche has it or not. My 2500 YukonXL definitely does. If you look at the shocks themselves the electronic OEM one's I've seen tend to have a lot of orange on them.
I was looking for a Rainier and decided on my 'burb (yukon XL) instead. But I like this site and check in regularly because it's loaded with good people and good information, even if it isn't all about our trucks. Personally I highly recommend picking up a factory service manual if you DIY and are planning to keep the truck for a while. It has instructions for just about every scenario you might encounter.