I put together a sort of how-to on this stuff that may be helpful to you, starting from scratch as you are. This gets into the tools as well as illustrating the techniques. That includes the right butt-end connectors and adhesive heat shrink. Don't let any of that concern you. Just check out the articles. Part 1 is tools and Part 2 is a step by step guide.
Solder or crimp? Debate on that can be fierce. After more than 8 years of daily commute riding, I have never had a crimped connection fail. How is that reliability accomplished?
The Anderson connectors are the ones in the foreground of your picture. Those are not my favorites and I always replace them. As @HumanPerson
noted above, an XT90 anti spark (aka XT90S) connector is pretty much the gold standard for this sort of thing.
Worth mentioning: You could buy an Anderson-to-Bullet Plug adapter and then have an Anderson-to-Anderson connection.
I would not go there as XT90's are head-and-shoulders better. That link also shows you an Anderson-to-XT90 adapter which, if you care concerned about working with hot battery leads, would turn that side into plug-and-play so you only have to do a crimp on your controller side.