The only effect that the month has is your ability to bank or use your points in case you have to cancel a trip.
Remember that you can bank 100% of your points within the first six months of your use year.
So you would generally want a use year that starts zero to five months before you normally vacation for that reason. For example if you had a June use year, but normally vacationed in May and you had to cancel, it would be too late for you to bank or even use those points. If on the other hand you travel in May but have an April use year and have to cancel, you would be able to bank all of your points or use them at some point over the next 10 months.
Some say this isn't a big deal and it probably isn't most of the time. I don't think it should be a major concern but if you are able to choose a use year, choose one that works best for you.
Good luck.
HBC