How to make a gmod server run 24/7?

1. You need to try to do it in virtual box. I recommend to installed debian 8 (jessie)
2. You need to find good VDS with AntiDDOS. it's not expencive, as you can find in first google page and as you can think.
why antiddos? - because some kids will indulge with dos in some programs like LOIC
for a start, i recommend to buy VDS with >0.5 cpu, >512MB ram and >=20 GB HDD
if you dont know linux well, i recommend to install some panel like OpenGamePanel)
in my vds i installed x32 binary(dpkg --add-architecture i386 && apt update && apt install ia32-libs)

Please read downloading tutorialandLinux tutorialin gmod website

Upd:about hosting on your computer - it's not expencive too)
I pay about 1,5$ for 24/7 hosted server on my computer and 4$ for VDS with antiddos