Texas Chili doesn't include beans or tomatoes, only beef, homemade chile paste, and a few flavorings. It's what Texans call a "Bowl o' Red" and tastes intensely of its two main ingredients. Take care to cook the chili at the barest possible simmer to avoid evaporating the sauce before the beef is tender. Whatever combination of dried chiles you use, make sure they're as fresh as possible.
I've never had True Texas Chili, my Grandad made a "4 Alarm" Chili that would blow the top of your head clean off it was so damn spicy, but that's all I've tried.