USB wifi dongle with AP support for Raspberry Pi

The first and the smallest is "USB Wireless N 802.11N Nano Dongle".
This chipset use rt2800usb module:

The id of device is VID_148F&PID_5370&REV_0101

Another great is "TP-Link WN722N" which use ath9k_htc module.
This is the best option for cost and wifi range. Totally must have:

The id of device is VID_0CF3&PID_9271&REV_0108

If your reputation do not let you to buy cheap adapter then buy "Alfa AWUS036NHA". This adapter is more expensive. It also uses ath9k_htc module. The advantage of this adapter is that you have additional USB cable option to extend the placement. Also you have addition cool gadgets to easily stick the adapter to the window or hook somewhere:

A lot of USB adapters is created nowadays but only a few works out of the box in a Linux environment.
Even less can work as and Access Point. So if you want to buy one I recommend starting from the driver side.
Search the driver module name in Google to find out which adapters can use this driver ;)

Here is the list of drivers which is used in manufactures who have ever created a USB wifi dongle with AP feature:

| Driver       | Manufacturer      | cfg80211 | AP  | IBSS | mesh   | monitor | PHY modes  | Buses |
| ------------ | ----------------- | -------- | --- | ---- | ------ | ------- | ---------- | ----- |
| ath9k_htc    | Atheros           | yes      | yes | yes  | no     | yes     | B/G/N      | USB   |
| libertas_tf  | Marvell           | yes      | yes | no   | yes    | ?       | B/G        | USB   |
| mwifiex      | Marvell           | yes      | yes | yes  | ?      | ?       | A/B/G/N    | USB   |
| p54usb       | Intersil/Conexant | yes      | yes | yes  | yes    | yes     | A(1)/B/G   | USB   |
| rt73usb      | Ralink            | yes      | yes | yes  | no     | yes     | A(1)/B/G   | USB   |
| rt2500usb    | Ralink            | yes      | yes | yes  | no     | yes     | A(1)/B/G   | USB   |
| rt2800usb    | Ralink            | yes      | yes | yes  | yes(5) | yes     | A(1)/B/G/N | USB   |
| zd1211rw     | ZyDAS/Atheros     | yes      | yes | yes  | yes    | yes     | A(2)/B/G   | USB   |

Related:
https://wireless.wiki.kernel.org/en/users/Drivers