When long-term provider cut off 3G in favor of VoLTE last fall, researched for some time. Preferred privacy over features, cameras etc. Of course, YMMV, but my humble conclusions, for whatever they're worth, if useful to anyone:
After looking at the specs and reviews, concluded that virtually all the basic/flip/feature/dumb-phones offered today were just cosmetically playing-dumb - they ran the same underlying "smart" operating systems (Android etc.) - so any semblance of privacy was out. Also, that the low-cost, no-name ones had truly bad user reviews - physical construction, OS reliability, and performance. So the alternative choices were a standard-shape smartphone, or a more expensive "rugged" flip-phone.
As far as savings, some pay-as-you-go people look for providers which offer refill cards which are regularly discounted at retailers. For low-data users, maybe check what mobile plan your local cable/satellite provider is offering (around here mo even after fees/taxes), or various less advertised MVNOs. "Free" phone offers are often attached to expensive monthly plans, so be aware. Shopping Nov-Dec last year there were many long running promotions - especially if you switched your number over. (The deals can get complicated, but as an example combining all of the above, a talked-about (surely expired) one was an iPhone SE 2020 for $49.99, minus a referral $25 discount and a $20 coupon (so $4.99), and while the process required choosing an expensive "unlimited" $60/mo plan, you could immediately downgrade to the least expensive 2GB-high-speed-data-included $30/mo plan (which is $27 with the regular 10%-off prepaid card sales). That provider (owned by one of the big three carriers) offers unlocking after 6 months, so if desired could switch to possibly save more.))
The only (semi) privacy choice would seem to be to buy a used, or find a rare new-old-stock, 3G flip-phone which uses a provider which isn't shutting 3G down. Maybe one box is hanging on a display hook forgotten behind newer items. Neighbor still uses a $5.99-on-closeout Alcatel One-Touch (BestBuy and Home Depot used to sell them around here). For him service works out to < $8/mo, and Tracfone has not yet warned him of any future 3G shutdown on the local network, whichever one it uses.
Never found evidence of the idea that some late-model sold-as-3G phones had inactive VoLTE capabilities which could be switched on.
