We will use 1B assuming she is able to get there in time, with pitcher there in case of total emergency. We use 1B mainly because if there is going to be an injury with a tag on a runner sliding in, we don't want it to be the pitcher.
I have never been real strong on the one throw rule. If another runner is on the bases and advancing, we will try hard to limit our throws. But if there is only one runner, then I don't emphasize the number of throws. I found over the years that if girls think they have to get it done in one throw, they tend to hold onto the ball too long for fear that an early throw will not retire the runner, and the runner often ends up diving safely back into a base.
We go through the various mechanics of what we want on rundowns, but philosophically we just tell our players that a runner in a rundown is out. We also tell our players that once we have someone in a rundown, I already have her marked down as an out in my head and I'm thinking ahead to the next pitch. That sends a clear message that running someone back to a base where they wind up being safe is never an acceptable result. And although this is the college level, I didn't do it any different all the way down to 12-U.