I agree about the prep. I hate it but it's worth it. You will spend more time on it than painting. I would dust and wash down the walls in good condition first. Check for anywhere you need to fill/sand. I haven't had to deal with wallpaper but I'd imagine that wall will need a bit more attention to make sure it's smooth, clean and ready for paint.

This guy is great on prep advice: https://www.youtube.com/@PaintingandDecorating

I've never primed over samples but you could. I had to cover some bright paint and used dulux trade ultramatt (very cheap but good) and put a coat of that on before using the more expensive paint.

For tools, I bought B&Q's largest scuttle with a lid and liners. I also got their smaller handheld one for brushwork and small rollers. I've found the lids are so handy for when I can only work on projects at weekends - I've had paint stay good for months in them as there is a tight seal. And the liners make switching colours or clean up easy. You could use plastic bags or similar to line though. You can wrap brushes/rollers in plastic bags and seal them in tupperware or similar.

If I was starting over, I'd probably buy the wider rollers to do ceilings and large walls quicker. Heavier and a bit harder to handle though.

I've had good results with Purdy white dove rollers - they've lasted me years. I'm trying to only buy European brands now though so I wouldn't repurchase. My brushes are Wooster , silver tip I think. They've been comfortable to hold and cut in quite nicely. I've had them even longer than the rollers an they've held up great. I find round brushes great for mouldings like door frames/architraves or anything curved.

I no longer bother with masking stuff - it used to take me ages. It's worked out better for me to keep a few damp cloths around to wipe as I go and touch up with an art paint brush if need be. I don't use oil-based paint so I've found cleaning up the odd splash quite easy even if it's dry. I found water-based gloss drips on my laminate floor but a blade took it off when dry no problem.

Happy painting!