For a PC, I would never go USB if I could avoid it. And with that generous budget, I would not limit myself to 150Mbps or even 300Mbps and would definitely get a dual band, and one with external antennas.
Sadly, the USB interface just has not proven to be reliable in spite of each new generation promising to fix the woes of the last. A quick perusal through any tech forum will show lots of users complaining about USB connectivity with their USB connected keyboards, mice, external drives and more. While USB 3.0 connectivity is more robust and stable than USB 2.0, it still has not proven to be as steadfast reliable USB 3.0 was supposed to be.
Except for keyboards and mice, I treat the USB interface as an interface to connect devices on a
temporary basis.
And also, when buying any USB device today, it makes little sense to limit performance and future abilities with a USB 2.0 device. If you must use USB, at least get a USB 3.0 (or even 3.1, if available) adapter for faster throughput and [theoretically and hopefully] more stable USB connection.
With that, I recommend instead of a USB adapter, use a PCIe adapter. A friend has an
Intel Dual Band 867 Mbps AC and it works great, Although pricy, it is well within your budget and with bandwidths up to 867Mbps, he can game, stream full HD 5.1 movies, back up his drives and more without any lags.
I've personally used this
Rosewill Dual Band N900 450Mbps PCIe Adapter on several builds with no complaints. I prefer adapters with multiple antennas you can orient in different directions. While these antennas are detachable so you can elevate them, they don't come with the necessary cables to do so. However, we have not needed to do detach and move the antennas for great throughput.
Finally, you said this was a new build - have you selected the motherboard yet? If not, there are several models with integrated wifi already. The
ASUS Maximus VIII Extreme, for example, is ASUS's new flagship Z170 board and is receiving excellent reviews. I note Overclockersclub.com concludes,
...the Maximus VIII Extreme comes to the table loaded for whatever you can throw at it. The robust hardware design, added functionality, and accessories bring the price up, but for those looking for the best, look no further.
Of course, there are models with wifi that don't cost $500 too. Like the
ASUS Z170-Deluxe which gets a nice Editor's Choice from TPU.