I have shipped well over 100 games and can say that most freight companies will sub contract out freight forwarders so even if you use STI, you will be getting a 3rd party involved or moving your game(s), that's just how it is.
As long as the game can be insured, then you'll be fine. If something happens, be prepared to go through the long and boring claim process.
Recently, I used coinopshippers.com which used fed ex freight. I was very happy with their level of professionalism. The game had to be palleted unlike NAVL/STI where they just furniture pad wrap it. Both ways work fine and its helpful to not pallet a game especially if the seller doesn't want to or can't pallet the game. Still, a pallet if used correctly offers a bit more stability for the game.
Tip.... if your seller has to pallet the game, look for the coke or pepsi pallets (they can be found behind grocery stores or drug stores sometimes). Those pallets are smaller, usually 36x38 and are perfect for most 19" monitor arcade game uprights. The 48x48 pallets are so f'n huge but will work with most 25" monitor uprights or larger cabinets. If you have a cockpit that needs palleting, most of the time I would have to build my own pallet so hopefully you're not in that situation.
The rate of shipping from Alabama to CA (to my residence) was arond $278. Insurance was an extra $30. Coast to coast, to a residence requiring a lift gate can get up to $450.
My fed ex freight experience was so positive that I will definitely use that method again. If you have any questions, feel free to PM me. Good luck.