@asifnaz :-
Do you know for a FACT that your 3GHz P4 is only 32-bit? There were so many variants, and different architectures of this CPU made, that we really need a bit more info on this point.
3 GHz "Northwood" and "Prescott" P4s were 32-bit. But with the final architecture release, "Cedar Mill", the 3 GHz model was 64-bit.....and sported Hyper-Threading, too (which effectively made it a dual-core), along with SSE3 instructions for better reponse.
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Dimkr's suggestion is a good one, if you're concerned about keeping everything bang up-to-date. But as peterw also says above, Bionicpup32 will still do mostly everything you want.....and the PPM 'archive' business ought not to be a problem, because as far as software installation is concerned, we don't tend to use stuff from the PPM that much.
Everything from the PPM is designed to work with the 'parent' Ubuntu release. But Puppy is NOT Ubuntu, and many things are done that little bit differently.......sufficiently different enough that a lot of things installed direct from the PPM won't work OOTB.
The usual recommendation is to use stuff from the "Additional Software" section of the forum, because anything posted here is built to work properly with whatever version of Puppy the author has packaged it for. And in all honesty, as far as Puppy itself is concerned, you need to get out of the mindset of "Must have the newest of everything all the time". Puppy's NOT perfect - nothing in life ever is! - but by design it's a darned sight more secure than most other Linux distros due to the read-only nature of its filesystem at boot-time.
No point updating purely for the sake of updating. Does yr Puppy still do everything you want it to do? If "Yes".....and it ain't "broken".....where's the point in trying to "fix" it? Updates can themselves end up breaking processes which previously worked fine.
I know there's many who can't understand this viewpoint, having had it drummed into them for years that for safety's sake, you "must run the very newest version of everything ALL THE TIME." No doubt I'll get chastised for my somewhat cavalier recommendations, but I'm used to it!
Mike.