I have used Verizon in the past. Their phones have limited usage overseas and they LOCK the phones. That means that if you are abroad for an extended period, you can either pay their high roaming charges or you have to be a new phone. You cannot use a VERIZON phone with another provider. Further, Verizon is rather deceptive and confusing about their plans and it is very easy with them to incur charges accidentally.
I rate them at the bottom of all service providers.
They also offer, at a discount to their customers, rental World phones if you don't have a phone that uses the EU system.
As far as the US, Consumer Reports rates Verizon's system number 1 in 29 out of 30 of the biggest markets.
My own experience — I drive some 100,000 miles a year all over the US, and have never lost service on the road with Verizon....how many can say that with ATT, Sprint, etc. For example, I check with people on a golf course in major cities who have NO service with others while I have four bars.
Now, and for many year, I've USED them all. I am always asking — in restaurants, gas stations, etc. — people on other systems who are on the road. NO ONE has the near coast to coast connectivity I have.