Budget-wise, I am looking to stay around $30k. I believe I am looking for the regular wheel base, the longest non-Suburban.
Technically, the regular ones are the Suburbans, they came out first in the 1930s and the others followed later.
Anyhow, there is a really nice 2009 Tahoe LTZ for sale on this forum with the L9H motor and some good upgrades, including larger brakes. It has very low miles and is super clean.
The L9H is probably the best LS engine out there for trucks in the 6.2 liter size. It does not have AFM and makes over 400 horsepower stock. It is my understanding that Chevrolet made only around 500-600 of these so they are even more rare than the 2500s.
Anyhow, for starters, my recommendation would be 2009 and up so you get the 6-speed transmission and Bluetooth. 2012-2014 has an updated navigation radio with a hard drive for storing music and playback and such. These same years have improvements such as Hill Start Assist, Cruise Grade Braking - Normal Mode, Powertrain Grade Braking - Normal Mode (2013+).
2010 and later 5.3 engines have VVT, variable valve timing which gives them slightly more usable power and better fuel economy. All of the 6.0 and 6.2 engines have had VVT since 2007.
By 2011 the AFM system was using improved components but still not as reliable as not having it. All 5.3 and most 6.2 trucks engines use AFM.