What to use after I wash my oil painting brushes? to keep them in good condition?

Baby oil.

Really.

The Bob Ross range does an odourless brush cleaner. Ask at your art store. Then you can get, or make a great gadget, that helps you clean your brushes, and the muck goes to the bottom of the pot, and leaves the clean cleaning solution at the top. You kind of swish your brush in the pot, and it has a mesh, or metal grill guard half way down. So your brush isn`t swooshing round in the sloughed off old paint. Or for cheapness, you could use turpentine, but that has nasty fumes, and is not recommended. When you have cleaned your brushes, pull them between your fingers to bring them back in shape. The brush cleaning pots are quite cheap, and sold at most art stores.

Getting them clean is the most important thing. Storing them upright like everyone is saying (otherwise the brush can deform and stay that way)

I have used normal hair conditioner to finish up washing.

Wash them in white spirit(turps sub) dry them off, if you are leaving them for some time wash them in warm washing up liquid and stand them to dry.I stand mine upright,some hang them bristles down.This has not harmed my brushes in over 50 years and was standard practise in both school and several colleges.Save the white spirit in a closed container,the muck will settle out and can be decanted off for re-use.

There is no need to do anything. Really clean brushes are ready to be used again. Don't be tempted to do anything to them except store them horizontally and protected from dust.

Mineral spirits (can also be called Paint Thinner by many brands)

The best you can use is a cleaner and preservative.

I use the one from old masters.