Rule of thumb says 3-4 per draught customer. Depends also if working with distributor or self-distributing, and of course how far outside of your backyard you send your beer.

number of kegs

Here is what I did and here is what I did wrong.
There is a thread on ProBrewer asking how many kegs per tap handle you need. I think 4 is number one response and 5 is number two. I went with 5 to be cautious. My goal was to have 100 taps in one year. That is a key question: how many taps do you think you can get? Thus I bought about 600 kegs. I bought 80 percent sixths and 20 percent halfs. Most folks told me to buy 90 percents sixths, but I wanted to be safe.
Where I failed was in the emptying a Fermentor. I should have added enough kegs to empty two fermentors. I had to do quick re-orders.
Another area where I failed was half to sixth ratio. I learned, too late, that your home market is likely to be half heavy. We are 40 percent half, 60 percent sixth. Another quick reorder.
Now I am fine. You will never need more kegs than when you are keg only (as I was for four months) because you cannot bottle any stock, you must have enough kegs.
Note: we get great turn around from our distributor, they will deliver kegs back to us any time, several days a week, if we need it.
Good luck.

Jeff, what size system do you brew on and what is your yearly output?

year one at Mother's

I have a 30 BBL system. We sold 2,331 BBLs in the first 7 months. Unsure how our year will end, maybe 5,000 BBLs? Wow, I cannot believe that that number is within striking distance. And we have not yet moved out of our home market. Lucky, lucky, lucky.