Non modular - All cables are attached to the power supply and cannot be removed. Once installed you have to figure out where to go with the unused cables.
Semi modular - Only the ATX and ATX 12V cables are attached to the power supply and cannot be removed. All other cables are attached later at your desire. This is kind of the happy medium between non modular and full modular since every build will need the ATX and ATX 12V.
Fully modular - All cables are unattached from the power supply. You have full control over which cables are needed.
I typically go for semi or fully modular. Since you don't have to store unused cables in the case, you have better airflow.
When it comes to the 80+ specifications that deals with how efficient each power supply is. Typically the higher the level of efficiency the better quality the power supply is. The better the efficiency the lower the heat output into the case. With the cost of power supplies today, I haven't gone with anything less than an 80+ Gold in over 5 years. For example, you can get an 80+ Gold Seasonic 550W power supply for about $60, whereas the same wattage 80+ Bronze is about $40.
80+ ratings from worst to best:
80+
80+ Bronze
80+ Silver
80+ Gold
80+ Platinum
80+ Titanium