Your bags should be checked through if you're on a single ticket.
I believe there are a couple of transit hotels which are airside (Aerotel or Ambassador Transit Hotel), but they may be a little pricey and you may have to book early to secure a room. If you get a room in these hotels, you do not have to clear immigration.
Think some people who have SKL access may use the sleepers in the lounge, but of course it's first come, first served.
Yotel in Jewel and the Crowne Plaza are both landside and connected to Changi Airport. If you book a room in either of these hotels, you would have to clear immigration first, and from there it's a short walk/SkyTrain ride to the hotel depending on your arrival terminal.
Not sure if there are any other options within Changi since I've never had to do an overnighter there!
Of course, there are many other choices downtown - perhaps others can chime in re: whether it's worth the trek with a 12-h overnight layover.