Why am I having trouble upon starting up? Chugging, up-and-down rpm, shaking?

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Only upon startup, and this doesn't happen every time. I go to start my car and notice the rpm will go up to 2000 - sometimes even as high as 3000 and back way down. And then it will teeter-totter up and down again, it will chug, the headlights flicker and it sounds like the engine is going to cut out completely. It feels as if it almost starts too fast and not 100%. It will shake while doing this and then it will settle out after a minute and run normal. This only happens upon startup and we have noticed it happens more frequently after the car has been running all day / is warmed up, as this doesn't tend to happen when we barely run the car or upon the first start up of the day. Sometimes it will start normal, other times it starts weird. We have checked the air lines and haven't noticed any sign of a hole or malfunction. We regularly take it for oil changes and keep up on maintenance as it has 201000 miles on it and is our daily driver.. What could it be??