I did lots of research in this area. I just switch my family over to Total Wireless, which is a brand of a Mexican company that operates Trac Fone, StraightTtalk, Simple Wreless, and a host of other small mvno. Verizon phones do carry sim cards for their 4G service. Most of these 3rd rate no contract companies run on the older 3G service, and Straight Talk does run off of Verizon's 3G network.. We have 2 LG G3, 2 LG G2, and a Droid Maxx which Total Wireless told me is not compatible with their service, Because we are trying to save some money we went with their least expensive phone, LG Optimus Fuel (look it up, man that hurt my heart, but my wallet will be happy).
I thought that I would be able to buy an unlock phone to use with Total Wireless, but after my research, it is clear to me that Verizon locked up their network pretty tight,t and finding a current phone with all the bells and whistles that phone junkies like me like to run on their network is next to impossible.