I have decided to revive my old LP collection with a turntable purchase. I am looking at the "under $1000" mark for my turntable (minus the cartridge). The records I do have are in decent shape, but one or two could use a good cleaning. I just do not have the volume of LP's to justify the cost of those need vacuum cleaners so I want to get a good hand cleaning kit.

Its easy to get caught up in snake oil in audio, and my lack of experience in analog leaves me somewhat open. I am a believer in "if it sounds to good to be true, it probably is" so that helps with caveat emptor. I need some recomendations for some accessories and cleaning equipment such as: (some of these I am not sure I really need or if they are really required)

LP mat?
Cleaner?
Brush?
Stylus cleaner?
Anti-static gun?
Cartridge alignment tool?

Any other small things needed?

Thanks,