Hello and welcome to JustAnswer!
What brand of oil filter are you using?
That one is likely ok. Many aftermarket oil filters don't have drainback valves, which allows oil to drain back out of the filter and top of the engine while it's off. This causes noises on startup. If you haven't had this noise in the past and have always used the Mobil filters, or are positive that these have a drainback valve, we should be able to rule out the filter. Otherwise, a Mopar(NNN) NNN-NNNNfilter would be recommended.
Depending on your climate you may get results from changing to thinner oil. For nearly all climates this engine calls for 5w20 oil. If you're in a very cold climate switching to 5w20 will move quicker on a cold start and may stop or lessen the noise.
If you do end up needing to replace the lifters it will run $80 for each lifter. The headgaskets will run about $100 (the heads have to be removed to remove the lifters). The labor to replace the lifters calls for 7.3 hours. Multiply that by the shop's hourly rate to get the dollar amount for labor.