Yep...I know that camera. I googled shutter lag and found a site that compares various brands. Among the worst is Minolta, which, it turns out, is what we have as our second camera.
Fujifilm and the Canon Rebel turn out to be much better. Casio is rated one of the fastest, but reviewers say it has a fuzzy focus, so that's no good---fast but fuzzy.
I've always liked everything Fuji company puts out, and I tend to like Canon. THis is going to be a bit of a search.