4.7 Starting Issues

I just bought an 02 Dakota with a 4.7. Has 175K Miles and runs and drives great except for what I think are fuel related issues. Runs great after it’s been running for a couple minutes, but it’s the start-up that is a pain.
First off, you need to cycle the key on and off a couple times to prime the fuel system. Three times after it’s been sitting over night seems to do it. Will then start right up like it should. If you don’t do this, it will crank for way too long before it eventually sputters to life.
Secondly, when it does start, it misses a little bit until it’s been idling for 15 or 30 seconds. Then it smooths out and all is fine for the rest of the trip. The longer it’s been sitting, the longer it takes for the miss to go away.
I am thinking the Fuel Pump may the culprit, allowing the fuel pressure to drain down while it sits---and then maybe weak enough to take a couple “primes” to recover. Am also thinking that one or more of the Injectors are bad, allowing gas to dribble out after the car is shut off. This would explain the lack of pressure after it sits, and also explain why it misses------has to get rid of all that excess fuel in the intake port before it will run smoothly. Maybe it’s both of these things??? Neither are fun or cheap to fix
Am I on the right track here? Which do you think it is? Advice or insight would sure be appreciated