best is to fly via budget airlines, its dirt cheap... so many beaches to choose from thailand to indonesia..you'll be spoilt for choice...singapore's beaches are all man made so not so exciting... look at these links tigerairways.com and airasia.com
These places are located in the burbs with many expats. However, these apartments are quite old and do not rent for that much. With your budget of 3600, you can find almost brand new apartments with hardly used facilities. newton/novena has some almost new apartments...of course, the newer apartment...
some rooms for rent have minimum rental period commitment. but 3 months rental deposit is quite normal. Best for you is to make many friends as possible when here, you will not be short of help from the locals or even residing expats. traffic is not a problem if u take the subway.
rents in district 9,10(orchard)are the highest in the city, with 1600 budget, look at the bukit timah/dunearn road(dist 11) area or newton/novena, distance is not really a fear factor here, it is mitigated by excellent public transport.
nowadays, acra is fully online, registration is fast because they just want you to pay up faster, they are also pro business, so the faster you register your company, the faster they receive a fee.