Hi,
I'll let others chime in on recommended districts... personally I like 11/12 but prices are so high here these days.
You may have already thought through these - what kind of place are you looking for? For example, what size of bedroom or living room are you looking for, is having a lot of space important to you? Do you want to be in a quiet residential area or someplace close to shops and eateries? I don't mean to overwhelm you, but these choices will help you narrow down and choose a place from all the options that an agent will present you -- it will save you time and effort when viewing.
If you're willing to take the bus instead of looking for a place near the MRT, you may be able to save some money. Living one or two bus stops away from the MRT seems to work quite well for most of my friends. You can walk/bus to the MRT when you need to and the rest of the time you can just take a bus direct to your destination.
In my experience (from our last two moves), we try to start viewing places about a month before we need to move in. View too early and you'll be at a disadvantage because the landlord won't want their place to sit vacant while waiting for you to move in... view too late and you'll be under unnecessary pressure to find a place fast. It may take about 2-3 full days of viewing (again, just our experience), that will still give you a good couple of weeks to prepare for your move after you've selected a place and signed the tenancy agreement, before you have to move in.
Even though the
property market is red-hot these days, don't let the agent pressure you into signing a lease after your first viewing. Particularly if it's your first time here, if you have time do look around at a few different units before deciding what you like.