I know you just use it for an example, but just to let you know a TL494 wouldn't be good for a push-pull converter, you'd want a current mode controller for push-pull. TL494 is completely obsolete, you'd use at minimum a SG3525 for voltage mode control of say a half bridge converter....
Anyway, back on topic...
For power transformers operating in the tens to hundreds of kHz range, you'd want an ungapped ferrite. A gap stores energy so inductors are gapped and transformers aren't. An example would be N87 from Epcos. As far as core shape, you'd typically want an E core of some type. Epcos EE, EF, ETD, EFD for example.
A gate drive transformer would be a similar material but perhaps a small ferrite ring or E-core would be OK. They don't have to be massive. N87, N30 maybe.
A current transformer would be a high permeability ferrite such as T38 (I might be wrong, this is something I have to look up every time and I haven't looked it up this time). Again, a small ferrite ring is usually OK. Make sure whatever material it is will be OK with the frequency. T38's only good up to 100kHz IIRC.
An inductor or flyback "transformer" (actually an inductor) needs to take a DC current without saturating, so it needs to store energy, so it needs a gap. You can use a gapped ferrite E core of similar material to a power transformer N27, N87 etc. The material isn't so important as the gap defines the permeability, or you can use a powdered iron toroid if the ripple current is small (i.e. continuous conduction mode). It's lossier at these frequencies but stands up better to the DC component of current as it acts as if it has a distributed gap. (Toroids are hard to gap.) Generally you'd just buy inductors of a given inductance and current rating when possible.
Anything that crosses the isolation barrier from mains side to what's supposed to be a safe side will generally be an E-core so that you can impement reinforced insulation properly.
[I'm giving Epcos as examples as they seem to be the most commonly stocked by Digikey, Mouser, Farnell, RS etc.]