Having been to saigon recently, i hope i can provide newcomers with some personal opinion and help.
Airport
from stepping off plane to immigration very short distance only. After immigration, head to the exit. There are money changer and can buy sim card here (although i didnt buy 100,000 VND).
Taxi are to the left of the terminal. Take only Vinasun and Mailinh (cost around 140,000 VND). Or you may also take bus 152.
Crossing the road
actually, very easy to cross. You maybe afraid the first time but just follow the locals. basically, cross when there are no cars or big vehicles... the motorcycles will swerve around you.
Taxi
as mention above, take only those 2. Plenty of 7 sitter cabs so got family no need worry. (not sure why sg dun have many) Starting fare is 12,000 VND..taxi ride around district 1 will not exceed 35000 VND.
* prepare small change as some taxi drivers may pretend that they don't have (e.g. taxi fare 25000 VND, they say don't have 5000 VND for you when you pay 30000 VND...)
Driving
One word..don't! i seriously don't know how the taxi drivers can drive in such a situation. Motor and cars coming from all sides, no signalling one. But interestingly, the days i was there..i didn't see any accident.
Food
try the street food...although i should say we Singaporeans may not be used to their food.. Things i like is pho, spring rolls and banh mi. You are sure to find vege in almost all the food.
Shopping
clothes at ben thanh and saigon square...but all very out of fashion one.. unless you buying sports tee. Can someone recommend where can buy clothes like in thailand?
Safety
generally, i feel quite safe there. no pickpocket or snatching. just practice the usual safety precaution...no jewelry, don't showoff your phone etc..i saw one woman who left her iphone in a shop..didnt realise until 5 mins later, the shop owner kept the phone for her and return it later.
*it's safe to speak chinese there...quite a few know how to speak...some maybe will ask where you from...just say you're from sg. Actually, some vietnamese looks so chinese that you can't tell them apart.
Travelling
vietnam roads are not very good...so lots of bumpiness. Also travelling is very slow...200+km can take you 6 hrs or more as most of their roads are 1 lane only.
that's all...i'll see if i can add a few more things.