Since Singapore is one of your destination, you should take STPM first. Use your STPM to apply for Singaporean universities as well as the public universities. I believe the better public universities (namely UM, USM, UTM, UPM) provide very good engineering degree. If you insist on private institutions, you should look for UTAR, UNITEN, UTP, MMU. There's no need to pay attention to the likes of KBU, KDU, Inti, Taylor's etc. etc. because there are just okay yet charge you for a ridiculous premium. Of course, if you have some ways to obtain scholarship for studying in Malaysia, Nottingham and Monash should always be your first choice.