Okay so you can wither pay for hosting or use free hosting (Forums might be down at times - vary with service)
These sites that I will post below I have used before.
Paid hosting:
1.
www.hostgator.com/
2.
https://www.godaddy.com/
3.
https://www.1and1.com/
You can look at this website for top paid hosting services for domains and such:
http://www.pcmag.com/article2/0,2817,2424725,00.asp
Free hosting:
1.
https://www.000webhost.com/
2.
https://www.freehostia.com/
* You can use ****** to find more sites*
When talking about creating a forums now you will need a open source forum software that you would upload to that domain and the forum can be accessed.
1. PhpB is most used and it is also free to use, you can also get free templates to start your forum out with (I highly suggest this as a starter:
https://www.phpbb.com/
2. MyBB - Similar to phpBB- might have it's different components but it is also free.:
https://www.mybb.com/
3. Simple Machines Forum - Very easy to use and set up - Similar to the ones posted above:
http://www.simplemachines.org/
These now are the ones that can be bought and are high quality forum software
4. Vbulletin (sa-mp.com runs on this software) - Has ALOT of components and features :
https://www.vbulletin.com/
5. Invision Power AKA IP Board - Very sophisticated software similar to Vbulletin - A lot of components and features:
http://www.invisionpower.com/apps/board/
6. Xenforo - Similar to the ones posted above:
http://xenforo.com/