Don't make it harder than it is
Except maybe a little harder.
I'm sure 10 times a day electricians have a conversation like "Well, you could just install GFCI receptacles" and the customer decides "Well I don't need an electrician for that".
And you can guess where this goes wrong. GFCIs aren't quite as simple as that.
Now, the key point to GFCI is that GFCI is not a receptacle. It is a zone of protection which protects any number of outlets or loads.
GFCIs come in many form-factors: GFCI+breaker, GFCI+switch, GFCI "just a GFCI" and of course the receptacle with which you are familiar.
Yes, obviously a GFCI receptacle protects its own sockets. But all GFCIs can protect, really, an entire circuit. Heck, in Europe, one GFCI protects the entire house - although that has some, um, compromises.
This is done via terminals that every GFCI has, called "LOAD". If a load or several loads or outlets has its hot and neutral wire attached to the "Load" terminals of the GFCI device, then they will be protected by that GFCI.
That is the only thing "Load" should be used for.
Of course the novice who is smarter than the electrician watches a Youtube video or two and is putting a GFCI at every receptacle, and using the "Load" terminals anywhere there are 4 wires. And then a ground fault trips them all, and they never figure out how to get them all reset!
So, the trick is to use one GFCI to protect the whole circuit.
Easy mode is to use GFCI breakers if your service panel has modern breakers available. These are more costly than receptacles, though.
The second option is to carefully map every circuit (via trial and error disconnections). Locate the first receptacle past the service panel, and put the GFCI there.
Either case requires identifying all the receptacles on that circuit and marking the receptacles (as relevant):
No Equipment Ground
Reset west wall this room
(the last line is purely optional). Making your own labels is legal so long as they are not handwritten.
And you are free to convert them to 3-prong outlets, even though they don't have a ground. Plain 3-prong outlets will suffice, but they probably need to be Tamper Resistant.
Or, grounds can be retrofit
But grounding protection is not as good as GFCI protection for humans.
Retrofitting grounds is allowed under certain fairly generous rules, and is handy when you have electronic equipment that needs grounding to suppress static electricity to reduce ESD damage.
Don't forget AFCI
AFCI is Arc Fault protection. It is designed to detect failing wire connections that are likely to start a fire. It "listens" electronically for the "sound" (waveform) of wire arcing. That can be just the thing for a house with old and suspect wiring, particularly if the wiring is aluminum.
(Other measures can help greatly with aluminum wire; I feel those + AFCI breakers make aluminum perfectly reliable).
AFCIs also can help with a child sticking 2 things in the hot and neutral slots, which a GFCI cannot detect if someone is being shocked between hot and neutral (the GFCI thinks that's just a normal load, but the AFCI notices the current curve isn't normal).