Currently we have AT&T. Can you use those phones with Total Wireless being they use Verizon's towers?
Or would we have to purchase new Verizon phones?
You will need Verizon phones, or CDMA phones. The TW website has a place where you can check the compatibility of BYOPs.
I believe by law CDMA phones have to support GSM but the reverse is not true unfortunately. That has always been a thorn in my side since Verizon versions of phones are always pricier. (I'm talking about the used/refurbished/older model) and it is the only network I can use at my home.
I will say that I, or anyone else in my house has never done the big cell contracts, we have always done Verizon MVNOs. I just recently switched from PagePlus to TW. None of us have ever had an issue with being de-prioritized, but we aren't heavy data users while out and about at places like WDW. My dd is currently on PagePlus with unlimited data and has no issues even after they are supposed to toggle her speed back which she says she doesn't notice and thinks they don't really do it LOL. Unlimited on these kinds of plans are usually something like you get 5GB at LTE then after that your data speed reduce to 3G.
We do use our data when in a remote area and it is spotty but that is due to lack of coverage, not being de-prioritized.
I also have never had an issue with customer service, any issue I have has been resolved via online chat or a phone call. There aren't that many issues that come up to warrant the need for me to pay for "better" customer service at double the cost anyway.
The only negative I can see is if you are the type who needs the latest and greatest phone and upgrades every 2 years. There was a time where you had to pay upfront for that but now some MVNOs are letting you put phones on payment plans, although you pay more than the buy it outright price. Total Wireless does that with some of their phones.