I drive 283 and 30 every day from Harrisburg to 202 ( you won't be going as far as 202). There is some construction on 283 around Elizabethtown but I think it is almost done. At 5:30 am (east bound)and 5:00 pm (west bound) I have only had lanes closed once in four months.
Get off I 76 at Harrisburg EAST exit (not sure of the number)and get on 283. You will get on 30 in Lancaster. 283 ends and blends into 30 so you don't really have to look for 30. It should be about 1 hour and 15 mins from Harrisburg to Coatsville.
Good luck.
