1) Make sure that Verizon has solid coverage everywhere they'll need a phone. That's much more important than which phone to use. The best phone, with no coverage, is about as useful as a small rock. I had a great phone when we moved. It was with Sprint. There's absolutely zero Sprint coverage in my daughter's house. Needless to say, I'm no longer with Sprint.
2) Avoid any phone with a battery that can't be replaced by popping off the back cover. The battery will go bad. Probably before you want to replace the phone, if it's not a cheap phone. A battery that you can replace by removing the back cover is in the $10-$25 range (depending on the phone). Labor to replace the battery on one that's not user-accessible is a lot more than that (and they'll make a nice profit on the battery too). Also, if the battery starts overheating badly, you can pop the cover off and shake or pry the battery out. If it's not easily removable, you watch the phone melt (if you're lucky and you're not watching a small bonfire).
3) Today I'd avoid any phone that can't accept a Qi charger receiver (or doesn't come with Qi charging built in). (That's wireless charging.) It's nice that all phone manufacturers (except Apple, of course) agreed on a single charging/data port. You can use anyone's charger on anyone's phone. But it's not nice that they chose the microUSB connector. That's probably the most often broken single component on a phone. Wireless charging (and wireless data transfer) makes the port almost unnecessary.
4) If your mother has a hearing problem (many of us "more experienced" people do), I'd avoid Verizon altogether. A bad GSM signal is a lot easier to understand than a bad CDMA signal when you don't have the hearing of a teenager.
The same goes for screen size. I tried to look something up on my daughter's phone yesterday, and even with my reading glasses it was a struggle. My phone has a 5.7" screen and I still need reading glasses for some apps. So unless they have eagle vision, a small screen is probably out.
5) Personally I'd avoid a phone that doesn't have an external SD card, but if your mother and sister don't plan on storing a lot of apps, pictures, music, video, etc., they don't need the extra storage space. (My phone is my "small laptop", so 128GB of storage is really not much, even though it's the most available these days.)
As far as which phone to consider, we'd have to know their or your financial considerations. Someone who doesn't need much storage or a large screen can probably get away with a phone costing only a few dollars (with contract - which means that you pay a lot more for the phone, but you're paying it in higher monthly bills, not up front). An S5? Why? Latest doesn't mean greatest. IMO, the M8 is a better phone than the S5 (and I've been using Samsung phones for years). What are the considerations? Price? Size? Picture quality? Battery life?
It's easy to tell you what to stay away from. It takes a lot more information to tell you what to pick.
Verizon makes it a bit easier than some carriers. Their stores usually have working models of the phones for you to try out, so they can look at the phones you haven't eliminated and see how they feel, how they look, etc. (A large phone is easier to read if your eyes are older - but more difficult to use with one hand, because it's harder to stretch your thumb across that larger screen.) Make your list, then let them go to the store and see what they like.
(Just in case you aren't aware of it, and you should be - all cellphone owners should be - the price you pay for the phone when you get a contract isn't the price you'd pay for the phone if you have to replace it before the contract ends. The discount for the contract is VERY steep. A $100 phone under contract can cost $600 to buy. [And you're paying about $900 for it in the increased cost of the contract over a no contract service.])
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