I've heard people having great luck with "painters pads" too, instead of a brush.
I've heard good-and-bad things about isopropyl alcohol, I tend to think it helps with a bit of extra cleaning so I still use it, but a pure distilled water rinse could be just as good if the washing gets all the grime. I use 90% iso because I can't find the 99% stuff. If you can only get 70%, standard rubbing alcohol, then you might want to mix it stronger like 80/20 instead of 90/10. I've also heard about people having good luck putting a dishwasher after-rinse in their cleaning solution too. Just one or two drops of Jet Dry, for example. I've not tried that myself as I prefer to eliminate anything that might build up over time - which I think the Jet Dry would do. That's the same reason I don't use the popular cleaning fluids. Even the D4 Disc Washer fluid that was so popular will leave a build up over time that requires the wood glue treatment (or other deep cleaning) to remove.
Distilled water is recommended for the rinse because you don't want any water softeners, fluoride, or other minerals/additives from your well/city water to dry on your albums. Spring water will still have minerals in it. So you want distilled, or something equivalent.
And to clean your needle, use a clean magic eraser and then use your turntable cue lever (if it has one) to lift the needle up and set it down onto the magic eraser. If you don't have a cue lever, then very gently place your needle down on the magic eraser and lift up. Repeat a few times and that should take care of any grime/build-up on the needle. If you have to use a brush on the needle then always go from back-to-front.
If you have dirty records, then you also want to clean your needle after every couple of records. Even with new, clean, records - doing the magic-eraser-dip is wise every so-often. That needle will pick up gunk from deep in the grooves.
Playing vinyl is a tactile experience, and I personally enjoy the cleaning/care of them nearly as much as the listening.