Is it better to buy STI ETF or Singapore Equity Unit Trust?

Why don't you consider buying bank shares instead? As the 3 banks have around 40% to 50% weightage in STI. It indirectly means that when the bank stock move, STI is expected to move in the same direction as them.
Next is that STI currently is still below 2008 high, but all the 3 bank stocks had already crossed their 2008 peak. Furthermore, bank stocks give better dividend than STI ETF. One of the reasons why STI underperform banks stock could be that STI comprise of several non-performance stock that drag down its performance.
Thus if you would to look at risk and return perspective, bank shares may be a better option than STI in the longer term.

Since you are just starting out your investment journey, any particular reasons why you would like to put your money into STI or Singapore Equity UT?

I would say that both aren't very optimal choices except for the fact that it is denominated in SGD and you have little or no FX risk when investing into such investments.

There are other options out there such as S&P500, NASDAQ, QQQ that may yield better returns with similar risk. Moreover, both options which you suggested have limited upside potential, and over weightage on a single geographical region and Industry (Financials).

Perhaps you should speak to a trusted financial advisor, or your close friends who have been investing in the markets to get a better idea of the various options that you have!

If you would like to, you may always reach out to me via my facebook at https://www.facebook.com/brandan.chen