So you expect someone to write you a free dissertation on screw thread selection? Frankly it's a bit lazy of you. Based on your information, nobody can say "The best screw thread for this purpose is ******" because you have given no detail about the purpose. How about things like:
Speed (rotational/linear)
Available torque input
Required force output
Load
Vertical/horizontal
Required positional accuracy.
What does "Several" mean? 15 times in lifetime, or 3x/sec?
What are the operating conditions? Heat, contamination, liquids, cleanliness requirements?
Required lifetime?
-handleman, CSWP (The new, easy test)