There are at least a dozen whole threads on here about different digital cameras. I won't try to summarise them, but i'll try and answer your question....
> Can you buy digital cameras that have decent lenses (as featured on old cameras where you can obtain great depth of field) and shoot instantly?
Yes
There are 1000s of good digital cameras. There are compact and SLR-type cameras with modern built-in lenses, which can give a good range of depth-of-field. There are DSLR cameras, each with a vast range of interchangeable lenses. A lot of people here tend to shoot with either a Canon or a Nikon DSLR. However many of us also shoot with compact cameras or even phone cameras.
As for shooting instantly, that depends on the start up time of the camera, the flash you may of may not be using and the focusing speed of the lens.