What is the best way to buy gold and sliver in Singapore?

Bullion or paper?

Bullion - Google for sellers based in Singapore. There are a few well known ones. If you are low risk taker, UOB does sell bullion at their main branch too but prices not too friendly and have to keep in original packaging if you want to sell back to them.

Paper - There are some sellers that offer precious metals savings accounts. Again if you are low risk taker, UOB also has precious metals savings accounts. Otherwise there is the SPDR Gold ETF available on SGX.