The difference in weight between carbon, aluminum, titanium, and steel frames will be--at most--a couple of pounds.
If you're really worried about catastrophic failures (which are going to be VERY, VERY rare in any material if it's a reputable manufacturer), go with steel. It will dent before it brakes. But really--if
My biggest concern about carbon would be that if you're getting a frame that really has a weight advantage over other materials (and again, you're looking at a pound, or MAYBE 2), you're going to be spending so much you'll get crap components for the same price. If you look at most manufacturer's sites, you'll see a progression that looks something looks like:
$1000: Steel/AL with Tiagra
$1500: Steel/AL with 105
$1750: Carbon with Tiagra
$2000: Steel/AL with Ultegra
$2150: Carbon with 105
$2500: Carbon with Ultegra
$3500: Carbon with Dura Ace
If you're moving into your first "real" road bike, I'd suggest you buy a high-quality gently-used bike (with any frame material), because within 1-2 years, you'll know what you want and want to buy a different one. Or you'll want to customize it bit-by-bit and spend 3x the cost of a new bike, if you're like most of us.
(I'm in the process of building an all-ti fully rigid hardtail that will do absolutely nothing better than a Karate Monkey but will cost me 3x-4x the price, when I'm done. So I may resemble that last remark)