I have tried both mineral spirits and turpentine. Both work, but I really like the turpentine better. Also, while you are at the store picking that up, get some "Japan" drier as well. I really like a drop or two in my Tru-Oil that is mixed up in an old ash tray when I rub it in.
I have tried the marbles in the bottle also. It works and just makes a mess as far as I am concerned. Buy the small bottles and just use them as you need them.
On another project I am doing right now, I am using a varnish that has a tung oil base. I got from some of the other finishers using this varnish that to help it keep better, just use some propane to displace the air in the bottle to keep it fresh longer. So that is what I am doing and it works. Of course the torch is not lit (read that again!) and I just let it blow into the bottle to displace the air and allow it to continue to blow as I put the cap on. But, don't say I didn't tell you to be careful. Before other freak out on this, I doubt if this is more flammable than the wet varnish and thinners we use as well. Just don't light the torch!