I use the standard "facebook for android" - which people refer to as as the "stock" app. I use it ecause it gives me a widget. I set it to refresh every few hours. It's nice having a quick little pop up to see what my friends are up to, without having to open anything. It looks really nice with a smoked glass theme.
Then I have "facebook touch" -- which doesn't have a widget but, allows much more UI and is (in my opinion) much better than the stock app. The major advantage - messaing to friends. Unlesss I'm just retaded, I could NOT figure out how to message with the stock app.
I put the app for "facebook touch" on the home screen right next to the facebook widget. I sometimes forget they are actually 2 different apps. This set up alliows me to everything on FB. Works great for me.
RE Alerts: I have FB set up (thru the settings on the PC site) to send me emails when I have a message. I get a notification in the top bar -- I actually get double notifications. A FB notification AND an email notification. I've noticed that the FB notification is WAY late. I'll get the email that someone commented, posted to my wall, etc... and then later (sometimes like 20 minutes later) I'll get a FB notification. It's not that big a deal to me as I don't use FB much. However, there is a common complaint that FB notifications on Android devices sucks. So, at least you know you're not alone. If you want good notifications - forget about FB notification. Go to the FB site thru your PC and set it up to notify you via email (use a gmail account for faster email polling).
The only thing I can not figure out how to do is to post pictures to a group page on FB from the device. Any help out there?