I think Minehut let's you host servers for free, I dunno if you can use mods, I just know it's (or it WAS) free..

You have 3 options:

1. Host a LAN server with mods on
2. Host your own server from home and install mods from that (This one is the hardest, also the most expensive of all three in the short run.)
3. Buy your own server from a hosting service and ask the helpers on there to make your server a modded server (The easiest way, but most expensive in the long run)

I could teach you how to do this pretty easily, as Tobbzii said, you can do it off your pc which can support anywhere from 1 to 7 people on an average pc without a great deal of lag, I do this all the time for testing, makes it so much easier to test things locally then to host a server for it (For different games) add my discord Godlikewars#1714 and I can explain all this np

You can host a server off your own computer however to be able to do this, you need to portforward your connection. There are plenty of youtube videos on how to do this.