I just picked up a new American oak 5 gal barrel several months back. I aged and RIS in there for 2 weeks as my first beer and it picked up plenty of oak, but a balanced amount for that style of beer.
Second beer I aged was a wheat beer that was 100% Brett fermentation and that spent 7-8 weeks and that too was a balanced amount of oak.
I am debating the next beer I put in it, but based on flavor contribution I know I can go 3-4 months minimum without over oaking it.
I wouldn't bother with Whiskey unless you want to both make your Whiskey more of a Bourbon and then you really want your next beer or two to have a whiskey flavor to it. There is no reason you cannot go directly to beer with a new barrel, however just taste it regularly and ideally start with a big, bold beer for the first batch.
Also, I waxed my barrel to reduce oxygen exposure since I plan to start aging a Tart of Darkness clone for many months in the near future.