Yes, I do this plenty. I have some SIMs I continue to pay for in cash (pay as you go) so I keep having access to the phone number, and it's not easily tieable to my identity (ie you'd figure out who it was probably through watching CCTV of me buying it which seems like quite a lot of effort, so good enough for people with lower threat models).

I don't know where you are but in terms of selecting a service or phone, I would just walk into a local shop and see what they have on offer. I can't imagine prices would vary that wildly between shops.

Edit: also no need to buy a whole new phone if you don't have a state threat model and just want to make it harder to track you for eg data mining corpos. You can just swap out the sim in your normal phone to receive texts then put your regular sim back in afterwards. Or if you have a dual sim tray. You could also anonymously buy an esim so it doesn't take up a physical sim slot.