For SQ it has to be KrisFlyer. It's not a good program for much else and anything but a saver F award is nearly extortion.

For LH, OZ, NH, and TG you can go with any program of your liking. TK does not have F class. LH typically releases F award seats within 2 weeks of departure. I also see NH a lot close in to departure. TG and OZ seem a little easier to score depending on the route.

UA is still the best when it comes to avoiding cash out of pocket fees, but now as fuel surcharges have declined significantly on many airlines then it may be worthwhile to consider other programs that charge fewer miles instead, but knowing you will still get tagged with some of the fuel surcharge out of pocket. How you're getting the miles in the first place would also change which program may be best for your situation. From credit card spend, where can you get the largest bonuses? From flying, is it paid F, C, or Y? Discount Y fares are heavily penalized in many programs when earning and paid F and C fares are heavily rewarded in some programs, so there is not one easy answer. You have to evaluate your own earn/burn situation and see what works out best for you.