Schiit... I'd certainly go with them instead if Fiio, and they'd have more power. I don't know if the Magni will drive the 250 ohm ones fantastically, but there is a good chance that they will. I didn't know the Magni was within your budget. I haven't tried it myself, but Schiit has a great reputation, makes stuff built to last, and a good return policy. Also, Made in USA, which adds to their coolness factor.
I'm not very familiar with the other brands, but Bravo's quality hasn't been great, and I'm not comfortable about mass production of an open-source amplifier design (personal opinion), but I'd myself go with the Magni for its support, cool physical design, and non-disposable build attitude.
Also, The Magni is a desktop amp. It will have more power than equivalently priced portables, which have compromises that desktop amps don't need to make (like size and power consumption). Portables also spend some of their money on charging circuits and batteries, and have to spend less on the actual amp sections. Batteries have a limited lifespan, and some amps may not work without a functioning battery, and inexpensive ones may not be serviceable. Ones that cannot be used while charging are also a terrible idea if you want to use them for an extended period of time. If you don't need portability, I'd usually recommend not getting one.
Unless you -really- want to start with tubes, I'd not recommend it for your application. They have a certain sound signature that, IMHO, doesn't work with games well. They are meant for, generally (YMMV), more relaxed music listening attitudes. I think games require more precision and impact, which match solid state better, especially in your price range. They also have maintenance, warm up time, are sensitive to vibration, and a less silent background, but those are minor issues. But ones to know about. And Bravo doesn't have a particularly good reputation for build quality.
