Thanks. It's nothing complicated and it's all probably all been said before.
De-anodise if need be with oven cleaner as detailed above somewhere.
You need to decide on quite shiny or mirror polished, some think they're the same thing but there's a clue in the name mirror polished!
If you want it quite shiny you can often just get at it with Peek or whatever, no need to sand (or not much). There's nothing wrong with that finish at all if that's what you're after.
Mirror polishing is a whole lot more work, especially by hand. You need to get rid of most if not all marks and high and low spots. Getting rid of low spots tends to take the time. In most cases you obviously want to keep the same profile and need to be careful of flat spots on curves etc.
So for sanding I've been using 800 grit to start with as the parts have been in good condition, if they weren't you'd probably need to start courser. You basically want to use as fine a grit as you can get away with or you end up spending needless time removing sanding marks plus you normally want to take as little metal off as you can.
You can always go courser if you're not shifting enough metal but not the other way around, once you've started course that's it. So start fine and go from there. Same with polishing if you have multiple grades.
Keep the paper wet from a bowl of water with a drop or two of washing up liquid.
Then it's just elbow grease. Low areas show up easy enough as the sanding misses them so you see patches of untouched metal. You needs to sand the surrounding until those areas have gone.
If you're using 800 or even 1000 to start with then it doesn't take much work on the other grades, I have 800, 1000, 1200, 1500 and 2000 papers. I've also some 3M polishing cloths, look and feel like J Cloths, nice on round surfaces and I have 400 to 8000 in those but you don't need them.
If you have deep scratches then you're sometimes better off improving them rather than removing them. Like my bar sleeve, there are still some marks but they're not obvious enough to make it worth completely removing and taking a chunk of metal off in the process.
Even with mirror polishing there's levels of it. If you want it absolutely perfect then you'd shine a light across it to show up any swirls and keep going until they're gone. But for parts that will go on a bike I'm not sure there's much point going that far.
Then it's polish. I prefer Peek over Autosol and prefer a terry cloth to apply & polish then buff with microfibre. I've recently bought Final Finish that has a very fine cut and is also a sealant. As with any polishing don't mix cloths up, don't want Peek on a cloth you're going to use for Final Finish. So a plastic bag with your polish and it's cloths isn't a bad idea.
Oh, I found that all purpose cleaner does a pretty good job at cleaning hands if you haven't worn gloves.
That's basically it, nothing clever or secret about it, just takes time. But once you get going it quite a rewarding thing to do, although once you've done a bike's worth the reward isn't as great and you're glad you're done!
Might be getting a second hand stem for the flat bar setup, if I do and I polish it I'll take pics of the steps.