Hi Bwjp, welcome to FlyerTalk! ^
It's actually quite simple once you pick out the important facts:
1. Only use miles for redemption in biz or first (award tickets, not upgrades). The only time I would use an upgrade is if I really needed the status miles to maintain *G, and it would save me a miles run later on...
For a comparison of redemption options you might want to
check out this thread: http://www.flyertalk.com/forum/singa...-spending.html
2. Only get saver awards (so you cannot redeem on the A380/77W)
Not sure how far ahead you need to book the saver awards as this varies, what's more important is a) how flexible you are with the date(s) -AND- b) how many people are in your party. You can log into KF and try some random dates and see how it goes. If it's just you then you should be fine.
Standard award is basically paying double miles (compared to saver) to get it. Not worth it unless you really want to fly in J on the A380/77W.
For saver awards your best bet is to take the SIN-FRA route on the 744 for European travel (though Amsterdam and a few others can be done on the 772) or SIN-FRA-JFK if you are flying to the US - East Coast. You can also fly to the West Coast via Japan on the 744.
One of the cheapest ways of flying in F to Europe is that 744 connection to FRA, where a 1-way award in First will cost you just 70,125k miles (82,500 miles - 15% online redemption discount).