If I am performing ghusl janabah under a conventional modern day shower in my home or even in a large hotel, can I perform ghusl without fully purifying myself first? Is it sufficient that I wash the parts of my body which have some impurities on them with the intention of ghusl of janabah providing that when washing in ghusl, I become confident that those parts become absolutely tahir in the process from all impurities. If I do the above is my ghusl valid?

Yes. Ghusl is valid.
You do not need to clean the impure parts before performing ghusl.
It is enough to get them purified during gusl.