I seem to recall from previous trips that at least in Tokyo the subways stop running pretty early compared to many cities.
I've found a cheap flight into Osaka but it lands about 10:15pm so this might limit my public transport options.
I want the absolute cheapest way into town. I don't care about convenience. I like slow trans and I like walking and carrying my backpack.
What are the late and cheap options? Airport limousine/shuttlebus or public bus or subway?
By searching the Official JR:west site from Kansai-airport to Osaka station it seems that the last train runs at 23:32 and costs 1190 JPY. Your ability to make this will depend a lot on how smoothly everything goes in the airport.
There are also night buses as you said. Depending on where you are going where are two options:
These both have the price of 1550 JPY but keep going further into the night meaning you can catch them for sure.
The last option is the Kintetsu nankai line which is right next to the JR station, which has a timetable here.
However the last train here leaves at 23:40 which might work as well. If you take the Nankai to the end station which is Osaka-Namba it has a few different costs depending on the train type.
920 JPY for Airport Exp.
1430 JPY for Limited Exp (Regular)
1640 JPY for Limited Exp (Super)
If you include Namba in "downtown Osaka", then the cheapest option is a local Nankai train to Namba. Cost is 920 yen, last departure is (currently) at 23:40.
If you want to go to Osaka station or somewhere farther north, then it really depends on where exactly you are going, but if the trip can be done on JR only, then the cheapest option is almost certainly the 1,100 yen Icoca & Haruka offer. For that price, you can go to any JR station in Osaka city, and in addition you can (but are not required to) ride the Haruka limited express to Tennoji. In your case you cannot take the Haruka since the last one leaves at 22:16, but you can take the last ordinary train at 23:32.
