It should be fine to use png-24. all modern browsers support them. However, one of the great things about the format is the variable transparency - if you want to use this, youll have to use MS filters to get it to work in internet explorer.
Be careful when using PNG for one of your customer's sites.... even though most newer browsers suppoort it, older ones do not and you risk having the customer ger very mad at you when they get complaints that the graphics are not showing up, or when they view the very expensive site you created for them on an older browser at one of their friend's house... not good.
If this is for yourself, and it is not mission critical to have 100% visibility, then yes PNG are smaller and have a better transparency then gifs.
I say stick to jpgs and gifs, it's amazing what you can render beautifully when you know what you’re doing. As one of the posters said above, only if you are looking for cool transparencies and you know for sure people with new browsers will be seeing the site - then and only then would it be OK. I've been to parties where I tried to show off some new site technology and it didn't work on some of my friends machines and they had to 'trust' that what I made was cool. Not a great feeling. Stick the basics and make them shine!