Advice on Cartridge and simple way to clean LP

It's been years since I have cued up an LP. Well, I finally have my rig hooked up. It is as follows -
- Cary CAI-1 Integrated Amp
- Rogue Audio Stealth Phono Amp
- Thorens TD-160 / SME 3009 S2
- JM Lab Electra 926 Speakers

I listen to Jazz, pop, alternative. I need to replace cartridge ($150-$200 price range). People have suggested AT-150 but can't seem to find these anymore. Any suggestions please. Additionally, can someone suggest a good ol fashion way to clean a record. Have read many threads here but all seem pretty elaborate. In fact, some of them made my head spin. I will eventually invest in a cleaning machine but that's down the road. In the meantime, i'm hoping I can do a pretty good job of cleaning by hand.