Have a look at this: https://store.open-electronics.org/index.php?route=offers/salescombopge&page_id=6
Its from a quick Google search.
A plus of going with a Pi is having ModemManager (software for controlling modems). Ive seen a working SMS manager connected to ModemManager written in around a hundred lines of Python. Or if you have access to a regex library its fairly simple to write AT command software yourself.
Going with Arduino or other MCU-based solutions is also a way, but the major budget element is the GSM board itself. And MCUs are way more limited.
If you go with a Pi3 you should be able to power it with a single 5V (havent checked exactly), remember to get at least a 3 amperes one. Thats slightly above 15W power at maximum draw.
edit
Havent looked through your question that carefully, Im too focused on embedded stuff and havent noticed a USB modem is an option. Get some cheap modem, but dont bother with all that usb mode switch stuff manually in my opinion. ModemManager is good enough for that. Or that shield with SIM900 - it uses UART.
As for screen output - thats nonsense IMO, unless you work with the kernel. You can launch a GDB session iver ssh or telnet. Or do any kind of stuff via ssh actually.
Also if you get a decent modem (like the USB one you posted) the Pi has WiFi and it should be possible to configure it as a router.
edit2 Blame me... Seen this in the feed and didnt check the question date.