Most of the cleaning solutions out there are nothing more than 20% denatured alcohol and 80% distilled water. I mix up my own most of the time to save money over buying those little bottles of cleaner in the store.
I also bought a big screen tv cleaner, its basically a felt type pad with a handle on it, a few sprays of the cleaner on the pad and you wipe across the screen. Otherwise the same solution and a soft cotton cloth, lint free, does the best job.
If you have a really dirty screen use something like a glass cleaner that is ammonia free, then follow up with the other solution to remove any residue. I have been cleaning computer monitors and tvs like that for years no problem.