(The good news is your computer can be updated to one
of those operating systems, but you would need to find a Tiger or
Leopard install disc. Apple doesn't sell these anymore, but they
can be found used.)
Your iBook G4 can't run 10.6 "Snow Leopard" (only an Intel Mac
can; you have a Power Mac). Your machine is likely to run
considerably better with Tiger/10.4 than Leopard/10.5, but 10.4 can
be harder to find.
The other question is software. 10.5 has more software packages
available, but if you need to run any old Mac applications from OS
9 or earlier in Classic, you must use 10.4. TenFourFox, however,
will work with either 10.4 or 10.5.
One other thing you need to consider is if your system is still
running 10.3.9, the memory also was probably never upgraded. Both
10.4 and 10.5 have higher RAM requirements; while 10.3.9 will run
with as little as 128MB of RAM, 10.4 requires 256MB, 10.5 requires
512MB of RAM and running TenFourFox on most modern websites will
not work well if you don't have 1GB of RAM.
Your iBook G4/933 has 128MB of RAM built-in, plus another stick
you can upgrade. "About Your Mac" should say how much RAM is
installed. If you don't have the maximum 1.12GB RAM already, I
would replace that with a 1GB stick -- RAM for that model of iBook
is very inexpensive and easy to find from Amazon and other sources.
Any 1GB PC2100 DDR SO-DIMM should work.
Once you install Tiger or Leopard, run Software Update
immediately (you may have to do this several times) to update your
computer to the latest version. Then you can run TenFourFox.