Don't park in the Toyota Center garage, it takes forever to get out of there. There's a lot of places around. One that I usually park in is on Caroline St. You head up Bell street past Toyota Center and turn left on Caroline. There's a parking lot on the left that's pretty small but right after it is another one with plenty of room. The entrance is really tight. It doesn't look like an entrance at all really. It's about $10 and only a couple blocks from the Toyota Center.
I usually just park a few blocks west for free. Never had an issue finding a spot, even during a packed house in the playoffs.
Parking is free after 6 in the streets. Its easier to get out too. I park on Caroline when I go to rockets games
You couldn't have picked a better game to experience for the first time. Smile and smirk. Walk out thrilled and happy.