The iPhone 4 on Verizon is a CDMA handset, no SIM card. The iPhone 4S has a SIM card, but only for international GSM roaming (technically, a TruPhone SIM will work for AT&T plus T-Mobile coverage in the US if you get the SIM slot "unlocked" for international service), again Verizon is a CDMA provider (excuse 4G LTE, which the iPhone 4/4S doesn't support) so SIM card doesn't matter for domestic CDMA service. SIM cards are for GSM providers.
PP uses Verizon's towers, so same native footprint coverage. No roaming, except at high costs. Check the map to confirm for your area. The only downside is that PP is now owned by Carlos Slim's empire (same folks responsible for the travesties that are Tracfone/Net10/StraightTalk)... and they now charge telecom taxes on top of the rates instead of combining it. That said, if Verizon's your ticket, Verizon's your ticket and if you want out, it's Page Plus or not much else. If you go that route, I'd highly recommend going Kitty Wireless for activation.