I'd say that it is your call so you can be as picky as you choose to be, but in general thunderstorms are often brief and scattered throughout the area, so they often may not even hit everywhere. You might look at the hour by hour forecast before deciding. The chance of a thunderstorm might mean you never go anywhere in some parts of the country or at least it seems that way at times.
On the other hand if you aren't in a hurry you can probably pick a really nice weekend for your first trip. Whatever you decide, have a good time when you do go.