You can certainly do better than Verizon as far as price goes. Do some research on MVNOs - Mobile Virtual Network Operators. They basically sublease bandwidth from Verizon, AT&T, and sprint (avoid the sprint towers due to coverage issues). My favorite one is Ting. I had Ting for a year or so before moving to a work-sponsored phone on AT&T. I previously had Verizon, Straight Talk, T-mobile, and P-Tel (great but went out of biz). Wifey has Cricket (AT&T owned MVNO on the AT&T network) because she needs international. If your friend is going to use lots of data, look at Cricket over Ting. If they only need basic call/text/web and will do data hungry stuff (YouTube or stream music) on WiFi, then Ting will be cheaper. I think Ting has a bill calculator on their website, so do the math and see what works better for their usage.
Most of the world runs on GSM phones (sim cars). Verizon and US Cellular (MVNO on Verizon network) use CDMA phones (no removable chip aka service not easily transferable between phones) IIRC. If you bring your own phone, make sure it is an unlocked GSM capable phone. BLU makes a good cheap smart phone. I had a BLU phone for about 18 months and was very happy with it for the price - $70 new not refurb. If you want an upgrade over that, the Moto series of phones are popular with the MVNO crowd.