House built in 1960's, upgraded to 200A service with new panel in 2009. Original wiring (2 wire w/not ground) and wall plugs are without ground prong provision and were not replaced. Want to provide personnel shock protection, but GFCI's trip immediately. AFCI's don't trip. If I install all AFCI's, will they provide any personnel shock protection (as well as fire protection)? Will a dual AFCI/CFCI have the same tripping problem?
Holy cow ! AFCI protection does NOTHING to prevent shocks! GFCI'S do, wether an outlet or a breaker. On 2 wire systems the national electric code allows 3 prong outlets because less than 6 ma imbalance in the hot to neutral will trip the circuit removing the hazard. The only requirement is the down stream outlets need to be labeled " gfci protected , no equipment ground". All the gfci outlets I have purchased for years has these stickers. Arc fault is looking for an arc and they would not see an imbalance unless a dual function. Go with GFCI if you are worried about shocks either breakers or outlets to protect from hazardous shocks.
AFCI does nothing for shocks --- Hold on.
I gather you are inside your service panel trying to fit GFCI or AFCI breakers. There are prerequisites to GFCIs being fittable.
Fix your multi-wire branch circuits
Search all the entering cables for cables that have 3 conductors (disregarding ground). Modern cables would be black white red, no idea on older cables. You are looking for cables where the neutral goes to the neutral bar, then there are 2 hot condutors each going to a circuit breaker.
On each and every one of those, no exceptions, the two circuit breakers need to be pulled and, the two hot wires landed on a 2-pole circuit breaker, and that reinstalled in your panel.
A 2-pole breaker will occupy 2 spaces. It is not to be confused with a duplex/twin/tandem/double-stuff breaker, which squeezes 2 circuits into 1 space. A defining characteristic of a 2-pole breaker is that both "sides" must trip together.
Once you have corrected all your multi-wire branch circuits as I describe, it will now be possible to contemplate GFCI breakers on those circuits. You will need 2-pole GFCIs for those circuits.
Search for promiscuous neutrals
When wiring the equipment safety ground, it's perfectly normal and common for grounds to spiderweb, loop, or interact among circuits. Say you have a basement lighting circuit, and an upstairs lighting circuit that brings a 3-way switch to the bottom of the stairs, in the same junction box as the basement lighting. Can the grounds from both cables intermix? Sure.
Not so for neutrals. Neutrals must remain entirely with their partner hots at all times. In the basement case, if you wanted a smart switch at the downstairs 3-way location, but the smart switch wanted neutral, you cannot steal it from the basement circuit. Not allowed.
Why is that? Neutrals aren't a big old spiderweb like grounds are. They are the normal path for returning current. Currents need to be equal in each cable or conduit, so what goes out must come back the same way. What's more, neutrals don't have fuses so if a neutral inadvertently returns current for 2 hot wires, it could overload, and you'd the neutral wire on fire! (The MWBCs above intentionally balance the circuit on opposite poles, and the 2-pole breaker enforces this.)
So you have to scour the circuit for places like this. I find them via careful inspection. The only formulaic way I can think of is to identify a circuit and plug a load (I love dollar store nighlights) into every socket. Then for the circuit under test, turn off every circuit, lift the circuit's neutral off the neutral bar, and power up all its hot(s). If anything powers up, it is powered by this hot and is poaching neutral from another circuit. The problem is, this tells you nothing about whether another hot is poaching from this circuit's neutral.. So you need to repeat the test for each circuit.
Hunt down actual ground faults
If the above methods don't make a GFCI happy, then you have something with a bona-fide ground fault. The place you start is plug-in appliances. Unplug everything, then plug things in one at a time until the GFCI trips. That's the problem appliance.
If all that does not fix it, then you have a genuine ground fault in the wiring, and you will need to find the middle of the circuit, disconnect it there, see if it clears, and continue to divide and conquer.