Pay cash and make sure you can register online anonymously. Most come with free minutes to start but make sure they are rechargeable with "refill cards" paid with cash or online using a prepaid credit card. Using a personal CC to recharge minutes defeats the purpose of anonymity.

It would be wise to make sure the phone comes with national coverage plan or excellent local coverage in the area you plan to hobby around.

I would also put a premium on selecting a carrier that has excellent coverage in the area you plan to hobby before thinking of an outside area code. If the carrier also has good coverage in an adjacent area code than the one you plan to hobby in, than go with that area code.

I bought a TracFone, a decent Motorola flip phone.  I'm on my second year with it.  I never use up the "air tme minutes" but have to top up the "months of service" on schedule.  If you like you Favs to recognize your number, don't let the month's run out or you might get a new number assigned.  
Most seem to have National calling plans, so area of service has not been an issue.
This was a very good move.  I leave mine turned off at other times.  Be sure you keep in a secure place.
I buy the refill cards for cash most anywhere, can add time outside the store using the phone & dispose of the used refill card in their trash!
Happy Hobbying,
skb