Making sure your records are clean is the first step, I'm sure a Discwasher is better then nothing. There's lots of debate about what are the best methods. I use an dedicated machine and I'm happy with my results. Clean 'em whatever way you like but clean records are where you need to start.
I use Audacity on a Mac to record. It's free and does a decent job.
I use Clickrepair to get rid of clicks and pops. I don't worry about any other noises.http://www.clickrepair.net/
I leave my recordings as "Side One" and "Side Two".
The whole process is close to not being worth it to me. Breaking up a side into songs would take me past that point.