Many people are able to go home with either a cane or using nothing. We can't say for sure about you, but here are some things to think about. Do you use a walker or crutches now before the operation? If yes, then you're more likely to need one afterwards...at least for a little while.
How strong is your other leg? Can it support you without the off-loading assistance provided by a walker or crutches? many people have arthritis in both knees. They have the worst knee replaced first but this puts a lot of extra load on the other knee until the leg operated on gets stronger.
You may find it easy to navigate your apartment but need to use an assist when outside or walking in the community. The long-term goal is to walk unassisted and pain free.