I will try to be as specific as possible, but please forgive if I leave out a few important details, I am not exactly a car expert

Recently, when accelerating from a stop, there is a one or two second rattle coming from what appears to be the front right of the car. I do not seem to hear or feel the rattle when accelerating while in motion (such as to overtake someone). I have tried to recreate it while in park/neutral and thus far I have not been able to do. It seems to go away when I pass 2k RPM. The car also tends to shutter a bit when this happens.

At first I thought it may be a misfire, but the engine is not really under an extreme load when this is happening. One thing I did notice is it is similar to the "auto-stop shudder" that happens when the computer adjusts the RPMs to either engage/avoid auto-stop feature.

I am also noticing the the car seems to change its mind on where it wants to idle a lot, more so than it used to i believe. Not so much a rouge idle, just more like "lets idle at 1000 RPM.. scratch that, lets sit at 1500 for a few seconds, ok now down to 900"

So the points that are probably most important:
Rattle appears to be coming from passenger side front of car/engine
Only appears to happen when accelerating from dead stop
goes away after 2000k rpm or so
Engine MIGHT somewhat stutter while it rattles..

Any helps or ideas would be much appreciated. Thanks!