Unless you want to allow for extended lounge time, 1 hr is fine if all on the one ticket.
If you arrive within 20-30 mins of departure of the outbound flight, or later, then SQ will put you on the next available flight (usually the next flight unless it is full).
If the alternatives you are talking about (1 hr and 3:20) are connections from the same flight into Singapore, I am not sure how a 100% chance of a 3:20 connection is more inconvenient than a 95% chance of 1 hr connection with a 5% chance of 3:20 connection.
What flight are you looking at into Singapore? There's some stats around that give you a good idea of reliability. If coming out of MEL, for example. the last flight, SQ 208 is the most unreliable. Of the top of my head, for the other flights SQ 218 tends to get in early, SQ 238 on time and SQ 228 early/on time. Not sure of SQ248 as it's relatively new.
Also beware of your connection - some of the SE Asia flights might be on SQ code on Scoot.