You don't need thinners to paint with oil. You can use linseed oil to make the paint more loose if you find it to be too thick. (This will slow down the drying a bit, but not that much.)
For cleaning your materials (brushes, pallete, etc.) you can use cooking oil to loose the paint, wipe as much of the oil off as you can with tissue paper, and then wash the materials with hot water and soap. Keep in mind that this doesn't work once you've let the paint dry.
A piece of glass (with white paper underneath) works great as a pallete and is very easy to clean (the way mentioned above).
Not making a mess is a completely separate matter, though. It depends how you personally go about using the paint (some people are just very messy, others are not). If you are worried about the paint going everywhere, just tape some newspaper around the place where you'd be working.