Hello there,
I'm an SCCM Admin for a school district as well, I only use Applications when possible, Really I App-V as much as possible. There are certain things you can't App-V but I would look into that more. Packages I use only for things like Registry changes and stuff like that.
Always try to get a MSI from the original Software Vendor, Create Transforms files with Orca, I have a tutorial on Windows-Noob about that and then deploy them Silently to Workstations.
Best of Luck!