I have recently gotten a record washing machine (a VPI 16.5), and I am just astonished how much difference it makes in eliminating background noise on my records. The VPI is pricey (~$500), but you can accomplish much of the same thing by hand, with a brush and a blend of distilled water, dishwashing liquid (like Dawn or Ajax in the US), and industrial-grade isopropyl alcohol.

And use a soft brush to clean the fluff off the needle before you play your records.

In my experience, you don't need to use any software to de-noise most records unless they are either scratched, or the original recording has tape hiss.