(ふっかつ) Resurrection, rebirth:use this about Jesus. Also can be used about a revival of some retro trend.
(さいせい) This means “regeneration” or recycle, but is most commonly used on a DVD deck:“Playback.”!!   TTT
(さいらい) Religious word – literal re-incarnation. Sometimes also used in sports – he’s the re-incarnation of Pete Rose!
(しんせい) Doesn’t fit this group. Usually used in politics. The new, improved, reborn communist party. The new, improved whatever.
かす(いかす) Can mean a doctor literally bringing a patient back to live i.e. after cardiac arrest.  However, it usually means “To make the most out of a limited resource or lucky opportunity.” So, you probably don’t have to worry about confusing 生かす with the other words.
(かえりざく) Literally, ‘to bloom a second time’:a revival of a trend or a second-start for a washed-up celeb.