Following some old advice, I normally use neatsfoot oil. I bought a 500ml tin from a horse tack shop some years ago and it seems very good.
I have tried good old motor oil (20/50 etc) and again it was good but was only really for the very low powered plinkers; not really recommended for higher powered rifles due to dieseling.
Mind you (a little off topic) I once relubed a Webley Service with modern lubes and the performance was dire. I then relubed using motor oil and performance was restored to as required .. the rifle has piston rings.
Silicon oil ... I have used this but tend not to now as I have a jar of neatsfoot to hand to soak washers in.
I thing Webley oils of old are simple motor grade oils (SAE30??) ... Weblube etc but may be wrong.
A tip I was shown once to get good oil penetration into the washer was to rig up a simple vacuum device based on a brake bleed kit. With the washer in the oil and a partial vacuum established, the oil penetrates the washer much more quickly.
Cheers, Phil