It's probably a good idea for both. A GFCI measures the difference between current into a circuit on the live wire and current out of it on the neutral; the ground wire just helps to make sure that in an electrical fault, the current isn't passing through you to ground. So a GFCI would be good in the places that current code calls for them: kitchens, bathrooms and outdoor circuits.
Same for the AFCIs: they help detect faults due to damaged wiring. With BX cable, that damage is less likely to be caused by driving a nail or screw through the cable than it might be with NM cable, but you still have the possibility of loose connections in your receptacles, or damage to electrical cords going to your appliances.
Another thing to consider: if you have older wiring, you may also have older breakers. If you're replacing some of them with GFCIs or AFCIs, you might think about having the rest of them replaced with newer breakers.
Arc-Fault Circuit Interrupter (AFCI)
An arc-fault circuit interruption device is designed to detect dangerous arcing within the protected circuit, and open (turn off) the circuit to prevent damage caused by the arcing. It does this using special circuitry to analyse the electrical characteristics of the circuit, looking for characteristics that match specific pre-programmed values. If the AFCI detects suspicious goings on, it opens the circuit.
AFCI breakers are typically combination devices, meaning they also provide similar overcurrent and short-circuit protection to a standard breaker.
Installing a combination AFCI breaker on a circuit containing knob and tube wiring would be a great idea, and could potentially prevent a fire.
Ground-Fault Circuit Interrupter (GFCI)
Ground-fault circuit interruption devices are designed to detect ground-faults, and open (turn off) the circuit when a ground-fault is detected. They work by using a current transformer (CT) to detect current imbalances between the ungrounded (hot), and grounded (neutral) conductors of a circuit. This blog entry might help you understand how GFCI devices work.
GFCI breakers are typically combination devices, meaning they also provide similar overcurrent and short-circuit protection to a standard breaker.
Installing a GFCI breaker on a circuit containing knob and tube wiring, probably won't provide any benefit. GFCI devices are designed to prevent electrocution, not to protect the wiring.
Combination AFCI GFCI Circuit Breakers
Circuit breakers that provide AFCI, GFCI, overload, and overcurrent protection are becoming more widely available. If you can find them for your panel (and afford therm), these would be the best option.
Best Answer
Go ahead with AFCI for the 15/20A circuits
As long as you don't have any shared neutral situations (look out for 14/3 or 12/3 cables entering the panel as you're wiring it), you shouldn't have any trouble putting your new 15A and 20A branch circuits on AFCIs. I would familiarize yourself with the way Square-D does AFCI trip diagnostics at least, though, so that you can understand how to troubleshoot a case where one of your new AFCI's is tripping.
If you do find a shared neutral or Multi-Wire Branch Circuit, you'll need to use a two-pole AFCI for it, though. This will also ensure that both hots wind up on opposite legs of the feed, preventing the neutral from becoming overloaded.
GFCI breakers aren't going to be useful for much, though
Since you have a 3-wire dryer feed and GFCI protection in most of the required places to begin with, you won't need GFCI breakers at all under the 2017 NEC, and will only need one for an air conditioner circuit (if present) under the 2020 NEC. You may wish to use one if that's the easiest way to extend GFCI protection to the basement, though.