It depends on which area of sound engineering you are interested in. Even sound engineering is broken up into many career categories in SG. They are mainly:
1. Live/Concert Sound setup - If you are planning to man a soundboard after your graduation then this is not the line for you. You usually have to start from the bottom up in this line to gain the experience needed. I started with this line when I was freelancing during my poly days. I was lucky enough to not just be a roadie to carry things here and there but was given a chance to actually be the engineer's assistant to help out with the sound balancing and stage monitoring. There are a few major players in Singapore for this line. These companies are usually tied up or sub-contracted by Event/Media companies who handles the main project/event. The list of events can range from concerts, D&Ds, big scale weddings, political meetings to even church masses. Working in this line takes alot of your time and energy. So expect to burn a few weekends and fats when joining.
2. Hotel Industry & Building Facilities - Mostly all 4-5 stars hotels in Singapore requries an AV Technician where you are in-charge of running audio-visual equipment in the ball rooms or function rooms. This is where you are usually hands-on with the soundboard. However don't expect much action as the range of events are usually limited to weddings or corporate events where the usage of AV is of the minimum. If the event is of massive scale or importance then they will just engage an external sound company to handle the job (like point 1 I mention). This also applies to big buildings and shopping centres with similar facilities as well (Suntec, Expo, Libraries, etc...), where you will be part of the Facilities Dept handling all AV related materials. Not too difficult of a job but you gotta accept shift work (esp for hotels). Also expect to have a broaden job scope when you are in the Building Facilities line.
3. Wedding Entertainments - This usually applies with Malay weddings where they engage for a small PA set-up for their karaokes or bands. These companies are usually family or self run, though the "bigger" ones do sometimes hire external help. This is also a perfect way to earn extra income during the weekends.
4. Educational Institutions - Similar to the hotel industry but usually the equipments are of a higher grade and quantity. The job scope will also be broader as you deal with much more than just manning a soundboard as you usually have to deal with inventory and equipment maintanence as well. Best working hours and job security are usually found in this line.
5. Production Houses - Go in to this line if you are more into sound editing or doing location audio for movies, tv shows, commercials and even corporate videos. You usually work in a studio environment, on location or just be in the editing suite. The downside to this is that you really have to work fast and smart to meet datelines for your clients. Working hours really varies in this line depending on your projects.
6. Broadcast Stations - Very very similar to production houses except you are doing it in a bigger scale company. Unless you have lotsa experience, be prepared to even work as assistants if this line happens to be your first job. On the bright side your resume will look much more impressive.
7. Professional Recording Studios - There are not many here in Singapore. Personally I would one day love to work in this line but most recording engineers here are usually those who open the studios themselves. So maybe one day, who knows...
These are the options that I know of so its all up to you and where you think your career lies in the near future after you get that qualification as a Sound Engineer. Its not as glamorous as some make it out to be...