I put new tires and tubes on my 2005 Giant Sedona LX. I was using Kenda Pathfinders with Bontrager self sealing tubes. This worked okay for a couple of years. But, l live in Colorado, and the goat head thorns are everywhere. My back tire finally wouldn't seal up anymore.
So, I got a pair of Bontrager H5 Hard Case Ultimate tires, and new self sealing tubes. These things are expensive, but it's worth it if I can actually ride for a while without flats. They are pretty nice to ride on, and can take up to 80lbs of air. I've taken a few long rides in thorn country, and no flats; so far.
Congrats. I don't live in goat head country but do run though lots of broken glass. I have been running a set of hard case plus (old name for their triple protection, now the ultimate) H2's on my primary commuter. So far have about 2400 flat free miles and still over half of the tread left on the rear tire. enjoy