I don't think it really matters. I have known a few people that started their learning on a 6-string and one guy I know bought a Conklin GrooveTool 7-string as his first bass. I personally started on 4-string, then to a 5-string, then to a 6-string, back to a 5-string and now back to 4-string again! I have been criticised that that my playing is too busy, so I have locked away my 5-strings and gone back to playing 4-string for a while. The idea is to simplify to maximise. It does feel sometimes like I am going back to basics, but I think it's a worthwhile exercise and I am already growing a new confidence. I find that I am utlising a smaller space to play my runs, scales and licks, but keeping it simple. And that's the trick when you are learning. Keep it simple...don't try to run before you can walk. Also, if you want to buy instructional materials such as books, CD-ROM's, DVD's etc...most will be transcribed mostly for 4-string bass at a basic to basic/intermediate level. By all means buy a 6-string if you want to, but you may be restricted when it comes to personal tuition.
My friend Stuart has been playing 6-string for 10+ years. He has never bought anything other than a 6-string and refuses to play anything else. I can remember one time a couple of years ago when we were at a small store trying out some amps and they did not have a 6-string bass for him to play with. He played on a 4-string Music Man Sterling and really struggled to complete his runs and licks as he depends very heavily on the extra strings that his basses provide. Stuart is a very fluent player, but it sounded like someone took a limb away from him. The way that you navigate your fingers and hand positions around the neck is very different depending on how many strings are on your bass. The best advice I can give is to cover your bases and start low to high and minimize your dependency for extra strings. Also, you will understand the geometry of the neck no matter if you may have to play a bass with fewer strings that you are less accustomed to.
There is no right or wrong depending on how many strings you want to learn with. Whatever makes you comfortable? You can learn just as quickly no matter what you use, but you have to commit to it for a while. Changing early on can really disorientate you and put you back in your learning.