My class earlier this year had everyone in their first choice straight of training (and we had people going to every base but Chicago) except maybe Detroit which took one extra month.
Don't sweat the NH bases too much. Things change so often especially once hiring picks up again that there's no reason to even worry about this.
Realistically speaking, unless you're in the pool now, the earliest you'll even be able to get out of training would be early-mid summer. No one knows what the vacancy will look like then, but whatever base you want shouldn't take more than a few months max.