China Mobile is cheap and has good coverage but the Internet is 2G & not 3G.
If you want 3G, you need China Unicom, which has bad phone call coverage in many areas. If you goto a china Unicom store I think they will try and get you to fill in forms with ID etc.
Ah well when OP mentioned iPhone and data I assumed requirement was 3G - ie China Unicom only - ie ID only SIM card purchase in CU outlet - but I might have misinterpreted.
Now as for China Mobiles 2G network - always amusing watching Chinese users growing old waiting for the 2G service to download data.
Oh and I forgot to mention recharging SIM card. This can be the most confusing and frustrating part of all phone services in China.
I currently have CU 3G SIM which works perfectly in my Australian sourced iPhone. I purchased this SIM card in Tianjin which is a city of 8 mil pop 140 km SE of Beijing. It is a monthly plan just like here - I bought SIM in TJ cause they had no min bal reqt to retain inter roaming capability - ie provided at least a few RMB still in bal then SIM card will still work in other countries (don't ask long story)
BJ CU outlet wanted guarantee of min bal RMB1,000 in account to retain inter roaming capability - same company - diff city - 140km apart - identical plan - identical monthly cost - welcome to China.
Now the tricky part - I regularly get my #1 girl in Nanjing to top up SIM for me - she trots off to CU office and tops up with her Chinese CC and I reimburse her cash each visit - perfect except no FF pts for me - impossible to use foreign CC to top up phone.
I am staying in Renaissance Beijing Capital Hotel in Chaoyang District with CU office right across street - I trot across street to office with RMB1,000 in cash in my hand to top up - after 10 mins arguing with staff there I leave with cash still in hand because they say is TJ number so they cannot accept payment to top up in BJ - WTF.
Had this many times with previous China Mobile SIM also - purchased SIM in BJ - many a time the top up cards purchased in CAN, PEK, HGH, NKG just we're not compatible - even bought China Mobile top up cards in BJ that were not compatible - funny thing was nobody could ever explain why this happens.
Sorry to OP for being long winded but China can trip you up so often -
always expect the unexpected.