Here is where I need the help... I have looked at websites, which talk
about dsp as if I already know what it is.. and try to sell me on a chip
or
kit or board which is supposted to do dsp.. but I am still trying to find
out how dsp can help me .....

That's a really big area and rather difficult to answer. Noise reduction is
a very
useful aspect of DSP. Depending on your rig, the filters can be helpful,
too.
As far as outboard DSP, you probably won't go too far wrong with a Timewave
DSP-599zx.
It's expensive, but the noise-reduction components are supposed to be quite
helpful.
A sound-card/computer approach that is very good is an older program known
as
DSP Blaster (db). I have searched high and low for a modern equivalent
software
implementation (something that can run on Windows XP, for example), and I
have
never heard its' equal. It has an agressive noise reduction component and
an coherent
CW filter which is hard to beat. I have found its' noise reduction unit to
be quite useful in EME.
The problem is Brian Beezley, the author, discontinued it. The program can
still be
found by a resourceful individual.

Onboard IF DSP is supposed to be the best - especially when combined with AF
DSP
in the same rig. I don't know which radio has the best perfomance-to-cost
ratio of such
an implementation.

73