What should I invest in if I already have a substantial amount saved up?

If that $10k may be subjected to last-minute deployment for other non-investment/emergency purposes, then I would not consider that $10k amount of money as "substantial".

Only invest in money you can afford to lose, otherwise you will consistently find yourself stuck in a predicament of whether to realized paper losses & lose long-term discipline to stay vested in the market.

Would suggest you continue to read up more on investment and save up money that is "specifically for investment" before moving on

If you are looking for investment, I would recommend you to take a look at Regular Savings Plan (RSP), I believe OCBC does offer that too, under their Blue Chip Investment Plan (BCIP). Basically how it works is every month, they will automatically take an amount which you decide (eg. $500) to invest in a stock of your choosing. For a start, you can consider STI ETF (top 30 blue chips in SG) or Lion Philip S-REITs ETF. Those will yield you about 3% annually. Not much, but decent enough and more than FD! You can also consider Singapore Savings Bond (~2%/year), but the yield now is pretty low for now, so the RSP might be a better idea.

Side note: I hope you are meeting your 360 criteria! You can consider SC Jump Start or DBS Multiplier alternatively as well :)