I played baseball for 14 years before switching to golf (im 28) and had the same problems in the beginning.
For your grip i would recommend an overlap grip. It is between the interlock and baseball grip. Basically grip your left hand like you would your bat, but instead of wrapping your thumb around point it down towards the club head. Now take your right hand and put it on top of your left thumb with your right pinky on top of your left pointer finger and have your thumb point down to the club head. It will feel a little awkward, but should be much easier to adjust to than the interlock method.
Now you didn't ask, but i just want to point out the two main differences in the baseball swing and golf swing when it comes to how your arms should be at the top of the swing. In baseball you were probably taught to bend your left arm and have the right arm up and out like a chicken wing. In golf it is the exact opposite. You want your left arm as straight as possible and the right arm tucked down into your body. Here is clip of my swing that kinda shows it at about the 4 sec mark (left arm straight, right arm tucked).
As far as weight shift, if you have a problem rocking too much, i would say start with more weight on your back foot so you don't rock as much and try and transition to your front foot during your down swing so that you could lift your back foot up after you hit and still be balanced.