Unless it's been fixed in the most recent updates (I've still got 377), "dialup only" seems to disable auto-updating regardless of your connection type on many systems. That's in the free version, anyway, not sure about the Pro/paid version.
If you still want auto-updates (which I assume you do) for defs only, go back to the default settings, auto for the defs and notify-only for the program. If you see a program notification and don't want to download/install yet, just close that box and nothing will happen ... I haven't gotten one of those yet, so don't know if it disappears after a bit if you just ignore it, like it did in 4.8 and earlier.
For connection type, your best bet (this worked for most of us unable to get updates, assuming the firewall wasn't to blame) is to uncheck both boxes in the connection-type section, and let avast determine for itself your connection.
As a side note -- if, from your description, the "program update is available" notification is that similar to the "defs updated" one, maybe Alwil should consider going back to using distinctive colors for those two.
