First; don't bother with any "cycle" grease, cleaners or lubes.
I use the cheapest car engine oil, 1 litre for a few £. For grease, marine waterproof grease, £5-10 for 500g. Ordinary car grease will be OK too.
The only bad experience with grease is I once greased my headset with a light brown lithium grease I found in a drawer. After riding all day in heavy rain, a rusty coloured liquid started to ooze out of the top nut. I took the headset apart and the balls and race were all rusty and pitted. I think it must have been like that for some time. So I cleaned it all out and reassembled (same balls) with Duckams Keenol and it's still smooth now.
For cleaning chains and sprockets, white spirits.
For cleaning frame and parts, damp cloth. Car wax/polish to keep off dirt and to make it easier to clean.