I see you're American. I'm pretty sure that
Stamford American International School is in District 19. The school typically has open houses each month, so you might want to check out their web site and see if one is coming up soon. I've been to an open house there and the campus is wonderful, but the tuition is pricey. It's one price whether you go 3x per week or 5x. There's no hard-sell tactics or anything that I've experienced. But, yes, it is a for-profit school as some might warn you, as are several other
International Schools and international preschools.
You also mentioned wanting to start him this fall/autumn. Keep in mind that starting in the fall is kind of a foreign concept for local schools in Singapore (whereas it's very typical in the USA). First of all, they don't know what "fall" is here because the weather is the same year around. Second of all, public schools are off here only in the month of June and in the last part of Nov and all of Dec. There are a few weeklong breaks between semesters as well and public holidays. Therefore, if you're interested in local school, it might be best to start him in July.