When I first started out shopping etc. all I had on the back carrier was an old backpack that didn't hold much and wasn't all that secure. Then the bike store down the street from me had those pannier baskets on sale for $2 (down from $20) so I got two and put them on each side.
What I do now is leave my left side open with a large tote bag securely in place while leaving the other side closed until I need the extra room.

One of the baskets I bought.

My old bike with the backpack

My current bike. Not the regular bag I take with me, but similar idea of what I do. I just have a larger bag usually.