There are several safety standards which people seem to be mixing up here.
SIL was mentionen, based on EN61508. This ranges from SIL1 to SIL4, although SIL4 is not usually used. This standard is appropriate for most functional safety problems, but is complex, so you may be better off with a simpler standard.
Another standard is EN954, which has been incorporated into other standards such as the Australian standard AS4024. I would recommend using this as a starting point, as long as it will comply with your local standards. This uses the concept of safety categories from B, then proceeding from 1 to 4.
A quick summary of these categories are:
B = Normal well designed electrical circuits
1 = As for B, but with enhancements for reliability
2 = As for B and 1, but with checking for failures
3 = Dual channel redundant, single failures will not cause loss of safety, as much failure checking as practical.
4 = Dual channel, single failures cannot cause loss of safety, accumulated failures will either not cause loss of safety or will be detected.
Old machines that were well designed would generally conform to category 1.
The appropriate category would be chosen from the risk assessment, and you can have different categories for different parts of the machine. For example, a limit switch detecting that a guard has been removed may only be category 1, but the emergency stop on the same machine may be required to be category 4.
Finally, the EU has brought out a new standard that will likely be adopted worldwide over the comming years. This uses performance levels rated from a to e, and are roughly equivelent in safety to categories B to 4. This standard was improved to take into account probability of failure, and so should be a better standard than the old EN954.
