Congratulation on catching it before the Rifa madness set in - they are metalized paper and notorious for giving off lots of magic smoke and occasionally a small flame when they reach a certain age. The cracking allows moisture ingress, which is the ultimate failure mechanism.
PME2616 capacitors are still available to this day, now under the Kemet brand, which will normally give several decades of continued life.
In most applications, a metalized Polypropylene (MKP) is a suitable replacement. As regards sub-type, the capacitor's position in the circuit is important, so it isn't possible to give an exact recommendation. If the capacitor is being used as an EMC suppression filter in an across-the-mains application, then it is important that a class X type is used, normally an [Edit: X2 X1 to match 630V DC rating], as they have thin metalization and are designed to be self healing on voltage spikes. If, on the other hand, it is being used somewhere inside the equipment, on a DC rail or pulse application, then it is important to not pick an X type because a thicker metalization is needed.