Only option for searching for printers is USB

Can you provide us 'hp-check' command output here.

ben@netbook ~ $ hp-check
Saving output in log file: /home/ben/hp-check.log

HP Linux Imaging and Printing System (ver. 3.15.7)
Dependency/Version Check Utility ver. 15.1

Copyright (c) 2001-15 Hewlett-Packard Development Company, LP
This software comes with ABSOLUTELY NO WARRANTY.
This is free software, and you are welcome to distribute it
under certain conditions. See COPYING file for more details.

Note: hp-check can be run in three modes:
1. Compile-time check mode (-c or --compile): Use this mode before compiling the HPLIP supplied
tarball (.tar.gz or .run) to determine if the proper dependencies are installed to successfully
compile HPLIP.
2. Run-time check mode (-r or --run): Use this mode to determine if a distro supplied package
(.deb, .rpm, etc) or an already built HPLIP supplied tarball has the proper dependencies installed
to successfully run.
3. Both compile- and run-time check mode (-b or --both) (Default): This mode will check both of
the above cases (both compile- and run-time dependencies).

Check types:
a. EXTERNALDEP - External Dependencies
b. GENERALDEP - General Dependencies (required both at compile and run time)
c. COMPILEDEP - Compile time Dependencies
d. [All are run-time checks]
PYEXT SCANCONF QUEUES PERMISSION

Status Types:
    OK
    MISSING - Missing Dependency or Permission or Plug-in
    INCOMPAT - Incompatible dependency-version or Plugin-version

warning: gentoo-2.2.0 version is not supported. Using gentoo-any versions dependencies to verify and install...

---------------
| SYSTEM INFO |
---------------

 Kernel: 3.19.3-1~exp1 #1 SMP Wed May 20 11:57:47 2015 GNU/Linux
 Host: netbook
 Proc: 3.19.3-1~exp1 #1 SMP Wed May 20 11:57:47 2015 GNU/Linux
 Distribution: gentoo 2.2.0
 Bitness: 64 bit

-----------------------
| HPLIP CONFIGURATION |
-----------------------

HPLIP-Version: HPLIP 3.15.7
HPLIP-Home: /usr/share/hplip
warning: HPLIP-Installation: Auto installation is not supported for gentoo distro 2.2.0 version

Current contents of '/etc/hp/hplip.conf' file:
# hplip.conf. Generated from hplip.conf.in by configure.

[hplip]
version=3.15.7

[dirs]
home=/usr/share/hplip
run=/var/run
ppd=/usr/share/ppd/HP
ppdbase=/usr/share/ppd
doc=/usr/share/doc/hplip-3.15.7
html=/usr/share/doc/hplip-3.15.7/html
icon=/usr/share/applications
cupsbackend=/usr/libexec/cups/backend
cupsfilter=/usr/libexec/cups/filter
drv=/usr/share/cups/drv/hp
bin=/usr/bin

# Following values are determined at configure time and cannot be changed.
[configure]
network-build=no
libusb01-build=no
pp-build=no
gui-build=yes
scanner-build=yes
fax-build=no
dbus-build=yes
cups11-build=no
doc-build=no
shadow-build=no
hpijs-install=no
foomatic-drv-install=no
foomatic-ppd-install=no
foomatic-rip-hplip-install=no
hpcups-install=yes
cups-drv-install=yes
cups-ppd-install=no
internal-tag=3.15.7
restricted-build=no
ui-toolkit=qt4
qt3=no
qt4=yes
policy-kit=yes
lite-build=no
udev_sysfs_rules=no
hpcups-only-build=no
hpijs-only-build=no

Current contents of '/var/lib/hp/hplip.state' file:
Plugins are not installed. Could not access file: No such file or directory

Current contents of '~/.hplip/hplip.conf' file:
[installation]
date_time = 08/20/2015 02:11:39
version = 3.15.7

 <Package-name> <Package-Desc> <Required/Optional> <Min-Version> <Installed-Version> <Status> <Comment>

--------------------------
| External Dependencies |
--------------------------

 gs GhostScript - PostScript and PDF language interpreter and previewer REQUIRED 7.05 9.15 OK -
 scanimage scanimage - Shell scanning program OPTIONAL 1.0 1.0.25 OK -
 xsane xsane - Graphical scanner frontend for SANE OPTIONAL 0.9 0.999 OK -
 cups CUPS - Common Unix Printing System REQUIRED 1.1 2.0.3 OK 'CUPS Scheduler is running'
 policykit PolicyKit - Administrative policy framework OPTIONAL - 0.113 OK -
 network network -wget OPTIONAL - 1.16.3 OK -
 avahi-utils avahi-utils OPTIONAL - 0.6.31 OK -
 dbus DBus - Message bus system REQUIRED - 1.8.20 OK -

-------------------------
| General Dependencies |
-------------------------

 libcrypto libcrypto - OpenSSL cryptographic library REQUIRED - 1.0.2 OK -
 python-dbus Python DBus - Python bindings for DBus REQUIRED 0.80.0 1.2.0 OK -
 reportlab Reportlab - PDF library for Python OPTIONAL 2.0 2.7 OK -
 python-notify Python libnotify - Python bindings for the libnotify Desktop notifications OPTIONAL - - OK -
 pyqt4 PyQt 4- Qt interface for Python (for Qt version 4.x) REQUIRED 4.0 4.11.4 OK -
 python-xml Python XML libraries REQUIRED - 2.1.0 OK -
 libusb libusb - USB library REQUIRED - 1.0 OK -
 cups-image CUPS image - CUPS image development files REQUIRED - 2.0.3 OK -
 error: libnetsnmp-devel libnetsnmp-devel - SNMP networking library development files REQUIRED 5.0.9 - MISSING 'libnetsnmp-devel needs to be installed'
 sane-devel SANE - Scanning library development files REQUIRED - 1.0.25 OK -
 pil PIL - Python Imaging Library (required for commandline scanning with hp-scan) OPTIONAL - 1.1.7 OK -
 python2X Python 2.2 or greater - Python programming language REQUIRED 2.2 3.3.6 OK -
 pyqt4-dbus PyQt 4 DBus - DBus Support for PyQt4 REQUIRED 4.0 4.11.4 OK -
 libjpeg libjpeg - JPEG library REQUIRED - - OK -
 libpthread libpthread - POSIX threads library REQUIRED - 2.20 OK -
 python-devel Python devel - Python development files REQUIRED 2.2 3.3.6 OK -
 cups-devel CUPS devel- Common Unix Printing System development files REQUIRED - 2.0.3 OK -
 sane SANE - Scanning library REQUIRED - 1.0.25 OK -

---------------
| COMPILEDEP |
---------------

 libtool libtool - Library building support services REQUIRED - 2.4.3 OK -
 gcc gcc - GNU Project C and C++ Compiler REQUIRED - 4.9.2 OK -
 make make - GNU make utility to maintain groups of programs REQUIRED 3.0 4.1 OK -

----------------------
| Python Extentions |
----------------------

 cupsext CUPS-Extension REQUIRED - 3.15.7 OK -
 hpmudext IO-Extension REQUIRED - 3.15.7 OK -

-----------------------
| Scan Configuration |
-----------------------

 scanext Scan-SANE-Extension REQUIRED - 3.15.7 OK -
 hpaio HPLIP-SANE-Backend REQUIRED - 3.15.7 OK 'hpaio found in /etc/sane.d/dll.conf'

-----------------------
| Other Dependencies |
-----------------------

------------------------------
| DISCOVERED SCANNER DEVICES |
------------------------------

device `v4l:/dev/video0' is a Noname HP Truevision HD virtual device

--------------------------
| DISCOVERED USB DEVICES |
--------------------------

No devices found.

---------------------------------
| INSTALLED CUPS PRINTER QUEUES |
---------------------------------

lpstat
------
Type: Unknown
Device URI: No destinations added.

--------------
| PERMISSION |
--------------

-----------
| SUMMARY |
-----------

Missing Required Dependencies
-----------------------------
None

Missing Optional Dependencies
-----------------------------
None

Total Errors: 1
Total Warnings: 0

Done.
======================================
I tried "emerge libnetsnmp-devel" to get the one missing package, but to no avail, it's not part of Gentoo/Funtoo's Portage tree.

 https://<email address hidden>/msg57062.html states that you need net-analyzer/net-snmp

Issue was unrelated; wpa_supplicant and dhcpcd weren't configured correctly. When I reconfigured those, connecting to network printers suddenly became an option when running hp-setup.
Thanks for the advice, though!