Down slowly (3 - 4 seconds) and explode up. That's what I've always stuck with and it works for me. Try different variations such as military, diamond, wide, pike etc. Work on increasing your reps over time and maintaining good form. That being said, what works for me may end up not working for you so experiment a bit.
As for back exercises, invest in a pullup bar or resistance bands. If this isn't an option, inverted rows are a decent substitute.