What cable companies make the best cables and sell them directly?

The best? Who knows as it’s very taste/system dependent, and then there’s budget that I don’t think you specified. Good news is pretty much all have generous trial periods, so read reviews and have at it! Cullen makes very good and reasonably-priced cables as does Audio Envy, Triode Wire Labs, Darwin, and Zavfino among others. One that flies under the radar and if you’re into silver cables is LavriCable — I’ve got a few of their cables and they’re great with both excellent transparency and musicality, which is a tough act to pull off. Best of luck.

If I had it to do over again, I’d buy used Acoustic Zen Silver Reference interconnects and Satori speaker cables (double barrel shotgun if you can bi-wire).  Buying good, used cables is one of the best bargains you can get in audio because you can sell them at little/no loss if they don’t work for you unless you happen to have a good dealer nearby.  If you can beat the AZ cables, buy them.  

I think VH Audio? is another standup, high-value option to check out.  So many options at this point it’s a bit mind boggling.  Read reviews to thin down the herd and then buy used and/or go with a direct seller with a good trial policy.  To me, both these strategies are almost identical price wise if you negotiate good used prices.