Shutter lag is what you're referring to I think Modeller and www.dpreview.com normally lists such things, as you have seen it varies immensely in compact cameras and in bridge models (to a certain extent in SLRs as well). All modern SLRs can be fully automatic so you don't have to do all the settings but some might say that removes the point of having the SLR if you let the camera make all of the decisions, up to you really. The advantage of the SLR with its bigger sensor is that you can get a shallower depth of field when you want it whereas compacts and evens bridges find this hard to do (with compacts impossible) as it is a matter of the physics of light. There is also another option which is the 'super' compact for want of a better description, such as the Canon G12, these are larger in the body than compacts but smaller than bridges, generally have better quality lenses (but shorter zooms than bridges) and can be fully automatic or allow a great degree of manual control.
The only real way to know is to go to an independent local camera shop where the people know their stuff and explain your dilemma, you may end up paying a bit more than you would with Amazon etc. but personal service costs.
PS. real, optical viewfinders (up to your eye) are a boon in bright sunlight as LCD screens can be very difficult to see.