Rank of Teacher
Ok, everyone has agreed that, for a beginner, the rank of a teacher doesn't matter. I do think, however, a certain caveat is in order. The teacher is VERY important. If you aspire to be shihan level one day, to get to the top levels of Aikido practice, then you will have to spend some, or even a lot, of time with a teacher of that level.
I can't think of a single instance in which a teacher of Sixth Dan or higher got to that level without training with a teacher who was at least that level.
There is a vast difference between the direct students of the various uchi deshi and the general student populace in terms of ability.
Let me put it this way... twenty years of hard effort with an average teacher will produce an average or slightly above average student. On the other hand, twenty years of average effort with a great teacher, will still produce an average student. But twenty years if hard effort with a great teacher will produce a really excellent student.