GFCI is an acceptable substitute for grounding. GFCI is good at protecting people from electrical shock. Grounds are good at protecting equipment from static damage. (it also helps protect people by giving fault current a place to go). GFCIs do nothing to protect equipment from ESD damage.
First, just sanity-check that your outlets aren't grounded. Inspectors make mistakes. Pop off a receptacle; if you see hot wire colors other than red, or if you see wires disappearing down a pipe, then you may have metal conduit, which is the ground. (There are no ground wires in any of my work; I use metal conduit.)
One of those cheap 3-light testers will tell the tale; 2 yellow lights means you are grounded. You'll want one anyway to test GFCIs. Ignore the "legend" listing what the lights mean; it's written for new construction, and does not imagine any of the problems that arise in old work.
It's perfectly legit to retrofit ground. You need only run a ground wire, on any viable route; you only need to reach any place which has a ground wire as wide as yours or wider back to the panel. However you're right, it's a lot of work, and human safety does not require it if you're using GFCIs - so option 2 is unnecessary for life safety.
Retrofit grounds for receptacles where grounds really matter, like refrigerators, freezers, PCs and delicate electronics. Refrigerators because we won't be GFCIing those.
GFCIs are able to protect downline outlets
The downside is that GFCIs will trip on any problem with a downline outlet. The upshot is you only need one GFCI device per circuit unless you want more than one; there are occasionally reasons for that.
GFCIs come in several forms: GFCI+circuit breaker, GFCI+switch, GFCI+nothing (these look like a blank receptacle with no sockets), GFCI+receptacle, and GFCI+receptacle+switch. All of them can protect downline loads.
So it is possible, instead of GFCI breakers, to simply install a GFCI receptacle at the first outlet location. Even if the outlet is a switch, they make GFCI+receptacle+switch devices where the switch can be wired separately from the receptacle. (you just don't use the receptacle).
In the case of a multi-wire branch circuit, the only viable way to protect the circuit is a 2-pole GFCI breaker.
That said, sometimes it's useful to use GFCI+receptacles and not use the downline feature (LOAD terminals). That can be useful if there are outlets downline that you don't want to protect (like refrigerators), or if somewhere downline is a wiring flaw that is tripping the GFCI - ideally you'd do a bug-hunt on the wiring flaws, but for expedience's sake you can simply do that. Most GFCIs allow attachment of 2 wires to the LINE terminals.
By the way, these GFCI breakers will take a lot of room in the panel. GFCI breakers are not available as "double-stuff breakers", so no doubling up in breaker spaces. I hope you got a nice big panel. If you didn't, you can fit a subpanel.
Also, there's no need to replace old panels which are Cutler-Hammer, BRyant, General Electric, Murray, or Square D QO. Those are a perfectly modern type of panel currently for sale. Kill FPE or Zinsco soon. Pushmatic panels are alright, but no longer supported - have those feed subpanels. Challenger panels just need their breakers changed to BR.
