In terms of nuclear staining, I haved used Hoechst 33342. How this dye differs from DAPI in terms of overall nuclear staining, I really don't know. They are almost identical when it comes to the excitation and emission spectra and both are excited in the UV. I know Hoechst 33342 is membrane permeable, so it can be used to stain the nucleus of living cells, but I believe DAPI does as well (not 100% sure). DAPI is not very soluble in PBS, so this is something to keep in mind.
Hoechst is extremely easy to use, you just add it to your cells and it only fluoresces when it is bound to DNA. For most cases you don't even have to wash it out. For microscopy it works great. The only problem I have found is that if you acquire images too frequently (every 5-10seconds) it can cause some phototoxicity over time (5-10mins). But this will depend on your setup and the intensity of your light source.
I have also used Hoechst to examine DNA content by flow cytometry. It requires a flow cytometer equipped with a UV laser. Again, this is really easy, all you do is incubate your cells for 45-90 minutes with the Hoechst and go straight to the machine. You just need to determine the correct amount of Hoechst (and the labeling time) needed to make sure everything is labeled.
Unfortunately I have never looked at apoptosis, so I cannot really help you there.
Check out these references for more information and protocols.http://www.pharm.uwa.edu.au/biaf/DNAstains.htm