Core Detonation: Never
Gas Warfare: Never
Information Warfare: Almost always
Mass Drivers: Never
Mini-Soldiers: Love 'em, except I never have them in TA.
Tidal Disruption: Occasionally
Traditional Warfare: A lot
My main attack is always informational unless the morale is above 80%. But there's a specific reason for this. I've been playing the Drathan's for the last month and they come with the soldiering +50. I also get the Tir Quan and other improvements so my soldiering is generally 18 to 19 and my tech is always higher. I very, very rarely don't take a planet with the first transport (I use 2B transports, not 3B). Occasionally you'll see a planet where my force is so overwhelming that I don't need to dink around with infomercials and I just do a traditional attack. That saves 800 BC. Also occasionally, especially against a race like the Torians or the Iconians, where they eithe rdidn't build any improvements or you're not goign to be able to keep any of the improvements anyway, I'll use tidal disruption. It's cheaper.
I think the native soldiering ability of your race makes a huge difference in invasion strategy selection, followed closely by the specifics of the planet....lots of population or little, lots of improvements or none, are they skilled soldiers or not, and how's their morale?