Which programs do I have to have running/listed in the Startup
tab?
None of them. You should have those that are useful to you and do
not hurt your performance.
I seem to have too many programs running.
Despite the common advice not to have "too many," I disagree. The
issue is not with how many, but which. From a performance
standpoint I'd much rather have ten such programs with little to
no effect on performance (and there are many like that) than one
that used lots of resources.
My view is that how long it takes to boot hardly matters. Most of
us boot once a day or so, and a few extra seconds, or even
minutes, just don't matter that much. When I get up in the
morning, I power on the computer and go get my coffee. When I
come back it's done booting. I don't know how long it took and I
don't care.
and it seems that my computer is running too slow.
That's a much more significant issue. It's possible that programs
that have started automatically and are running in the background
could be affecting your performance.
But don't just stop programs from running willy-nilly. What you
should do is determine what each program is, what its value is to
you, and what the cost in performance is of its running all the
time. You can get more information about these with google
searches and by asking about specifics here.
Once you have that information, you can make an intelligent
informed decision about what you want to keep and what you want
to get rid of.