What form of generators could a pre-electric civilization (think USA before Edison and Westinghouse) develop to provide for the electrification of society?
Purely electromagnetic ones. Plenty of AC motors are built without any permanent magnets, because the rotor can be magnetized either entirely by induction, or by running current through a commutator to power magnetic coils. Similarly, a generator can have a stator composed entirely of non-ferromagnetic electromagnets. You just wire it up so that the generator's own output energizes its own stator coils. You need a tiny bit of starter current to set up a seed field before the generator becomes self-sustaining, but that's easy to provide with a chemical starter battery, or a capacitor.
(Note that the Earth itself is just such a self-sustaining dynamo. The geomagnetic field is not ferromagnetic in origin, so we're all still safe from space radiation.)
A Kelvin water dropper generator, or other influence machines operating by electrostatic induction, might also be viable options. Unlike most static electricity generators (e.g., van de Graaf generators, such as are referenced in EDL's answer), a Kelvin water dropper doesn't have any moving solid parts or sliding contacts, which means it would require far less maintenance and could easily be scaled up to very large sizes and voltages. They would be ideal for constructing DC hydropower stations, with none of the mechanical complication of an autoinductive electromagnetic generator. Other influence machines involve moving parts, but no sliding contacts, and so would be no more problematic than normal electromagnetic induction generators. These kinds of devices, however, produce far less power than electromagnetic induction generators, so I would expect them to be rapidly superceded by autoinductive electromagnetic generators as soon as electromagnets are discovered--perhaps sticking around as an alternative to batteries or capacitors for generating the starter current.
The differences is everyday life would be minimal up until very recently. There would be no fridge magnets, and cheap mechanical speedometers for motor vehicles would be harder to design... but that's about it. The lack of ferromagnetic materials only really becomes a problem when you want to design tiny efficient DC motors. So things like cheap motorized battery-powered toys might take longer to develop, if they aren't just completely absent, and things like hard drives, floppy drives, and CD/DVD drives would be bulkier and less power efficient.
Of course, magnetic compasses wouldn't work, and that would imply some major changes in the history of navigation, and thus the history of the world... but there are ways to work around that, and while it changes some people's lives significantly, and changes the broad strokes of history, it doesn't have a whole lot of direct impact on the everyday lives of most people. After all, even in later industrial times, just prior to widespread electrification, what fraction of people in urban society ever regularly made use of a compass?
As pointed out by Zeiss Ikon in a comment, there would be no hard disks, floppy disks, recording wire, or magnetic tape, either. Fortunately, that's not a problem for the initial development of computers--it makes developing rewritable persistent storage media harder, but there are plenty of volatile storage options, which have been used in historical devices, that do not depend on magnetism to function--things like acoustic delay line memory and triode flip-flops. Electret-based technologies might be developed in place of early magnetic storage systems for temporary off-line data storage; the reduced stability of electrets vs. magnets would make such technology unsuitable for archival or distribution in the manner of, e.g., floppy disks or magnetic audio tapes, but could serve as medium-term memory to reduce the need for expensive active RAM. This isn't technology that was extensively researched in our reality, so it's hard to say exactly how far it would go.
Expect, however, to see a lot more usage of things like punched tape and capacitive disks on the way to the development of optical storage. Until the advent of re-writable optical storage, home computing would lack any equivalent of our hard drives or floppy disks; anything you want to save would have to be saved immutably, and if you want to edit something, you would do so by loading the old copy, changing it in memory, and writing it to new storage. Backups become an inevitable side-effect of working with digital technology, rather than something everybody always forgets to do!
And eventually, someone will develop floating-gate persistent flash storage, which is, in fact, electrostatic, rather than magnetic, in function anyway.