By law, all Singapore ISPs have to provide internet access though proxy servers. So, theoretically at least, all internet traffic can be monitored and unsuitable sites blocked. The reality of course is that to monitor everthing is totally impractical and any sites blocked are largely symbolic. If it really worried you there are apparently ways and means of using other, non singapore, proxies
As for cost. It is up to you. Starhub provides a free dialup service and the other has cable modem service. ISP's have plans ranging from abt $10 for abt 10hrs up to abt $100 for unlimited. In addition Singtel (Magix) and PacNet have ADSL Services and SCV (Sing Cable Vision) has a cable modem service. SCV charge $66 for unlimited access if you are also a TV subscriber. The ADSL services are priced either according to time or data usage