Actually, I've found coffee makes me too jittery to focus (my hands shake on the weights, not ideal). The crash after ruins the rest of my day too. I just stick to water and a good warm-up now.
Yeah, the jitters are real. I once spilled my pre-workout coffee all over the gym floor because my hands were shaking so bad. @john697 has a point with timing, but if you're prone to shakes, no amount of waiting helps. I switched to cold brew, it's smoother, but still not for everyone. Honestly, water and a solid warm-up like you said is the way to go, no crash to deal with.
Sandra_lee93 makes a solid point about the crash, that post-coffee slump can wreck your afternoon. I've had better luck timing my coffee at least an hour before a workout, letting the initial jitters fade. For a lighter boost, green tea works without the same shaky feeling for me.