No Staal or Tudose patterns as options?! Just kidding. Those are actually what I would consider to be deviations off of the main 'Star' pattern. I actually use those a lot now, as they have their very helpful place as plan-b variations, and they can help with survival -as well as point-pressing- if used properly.
I chose 'mix'; however, my base pattern is the Star. The reasons for this are simple:
1) The Weave is often simply necessitated by fireballs at the beginning.
2) The Weave has its merits, when used properly, in terms of both survival and point-pressing:
-In terms of survival, if you think you won't be able to get back down to the bottom hammer because of some middle-spawning fireballs, the Weave can help you avoid this.
***However, I'm starting to believe that 1) being able to judge ahead of time whether or not you will actually get blocked off by a fireball is nearly impossible in most cases, and 2) where the Weave would help you in this manner, the Staal pattern is actually nearly as good in terms of survivability, as well as nearly equal in terms of average points gained (there are usually more points wasted in the Weave waiting to grab the top hammer, where in the Staal pattern there is usually more time wasted clearing the last rivet by the bottom hammer). However, I admit that more testing needs to be done on this point.***
-In terms of pressing, I think the Weave can be superior to the Star when many fireballs spawn up near the top. This allows you to quickly (hopefully!) get to the top hammer with the potential to smash a ton of fireballs and then quickly finish the screen, whereas, in the Star you'd be stuck waiting around by the bottom hammer for fireballs to descend, and you'd probably get poor smashes anyway.
3) Finally, the reason why I use the Star as my base pattern, is that it is ultimately more adaptable to more situations. If all else fails, this pattern is more easily dropped for 'free styling'. Some of my suspicions about how the Staal pattern compares to the Weave -as well as the fact that you can't do the Tudose pattern while also doing the Weave- contributes to this decision as well.
One final note, what Mark said about the Weave is crucial!!! In order to do well at the Weave, you need to know how to efficiently use the top hammer to maximize your survivability. The fact that this takes quite some experience to gain may factor into this poll, in that newer players may not yet be able to utilize or understand the merits of the Weave because they have yet to develop those skills and see it for themselves in practice.
EDIT: For anyone wondering what I mean, I've attached some pictures of the 'Staal' and 'Tudose' patterns below.