Have you just installed the proverbial "Orange Turd" oil filter. Fram oil filters are notorious for reducing the oil pressure enough to cause lifter noise on cold startups. NAPA Gold (Wix), Purolator, and Motorcraft are about the best oil filters out there. I can post a review of almost all the oil filters out there if anyone's interested.
If that's not your problem, your valves may need to be adjusted (if they're adjustable). The rattling could be the rockers tapping the top of the valve stems. They can make a lot of noise when they need to be adjusted.
1992 Ford Bronco
E4OD- B&M Stage 2 shift kit
Full 3" stainless Bassani Exhaust
32" BFG's/stock suspension
"No replacement for displacement."
"Our lugnuts require more torque than most Honda's produce!"