Cleaning metal bits

[Ploshkin]

I posted a picture of this on another thread when I first rediscovered it.  It is my first sewing machine, dated about 1956.
I put copious amounts of sewing machine oil on it and the mechanism is now working smoothly and the surface dust and gunge has cleaned off.  I have decided that I won't attempt to thread and stitch with it because I don't want to risk breaking the tiny needle which I would imagine would be impossible to replace.
I just want to clean up the bare metal bits which have a bit of surface rust.  I am currently using sewing machine oil and very fine grade (000) steel wool.  Is this the best thing to use or is there something better.
I don't actually know to what extent it is possible to clean it so I don't know what I am aiming for.  I don't mind how long it takes but don't want to be trying to improve something that's as good as it is going to get.
I would be grateful for advice.
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[Efemera]

https://www.amazon.co.uk/Peek-Y048-33200-Box-Tube/dp/B000TROMR6/ref=sr_1_6?adgrpid=61617695428&gclid=EAIaIQobChMI1auLs_rD5AIVFODtCh2QSQw6EAAYASAAEgKy-fD_BwE&hvadid=259086003777&hvdev=t&hvlocphy=1006928&hvnetw=g&hvpos=1t1&hvqmt=e&hvrand=16487802392290873131&hvtargid=kwd-296865052309&hydadcr=18510_1725399&keywords=peek+metal+polish&qid=1568039553&s=gateway&sr=8-6

[LeilaMay]

I use Autosol - pick up a tube in Halfords 
https://www.halfords.com/motoring/car-cleaning/shampoo-polish-wax/autosol-metal-polish-75g

[Roger]

I’m a big fan of autosol too. It’s gently abrasive like a creme cleaner. Gets metal looking amazing tho!

[Bodgeitandscarper]

I've used Autosol too, along with steel wool.

I think a lot of these machines were chrome plated, and if that has rusted away, you won't get it super shiney. 

[Ploshkin]

I'll give the Autosol a go, thanks.  It's improved greatly just with steel wool and oil.

[wrenkins]

Another vote for Autosol here. Used to use it on my bike rims and still use it on whatever needs it. My 28k was the last job and it came up a treat. 

[mums sewing machine]

Oh I love this forum!
Just been and bought some Autosol - fingers crossed!
Thanks for the recommendation x