Are you looking for a vps? or just a server to run Terraria? There are a bunch of places that have cheap Terraria servers. Most large companies will charge more for their servers however, they will have more staff the help you if there is an issue with your server. Make sure to read real reviews or maybe find a someone who is renting one of their servers to see their opinion. I found a few places that host Terraria servers and some places that have vpns you can check out. I haven't used any of these hosts so be careful.
^These are all pretty big hosting companys if you dig around you can probably find cheaper ones.
VPS Hosting:
http://www.nfoservers.com/order-virtual-dedicated-server.php
^I also have no idea if they're good
Dedicated Servers:
I'm currently using Simplehost for a minecraft server. They rent dedicated servers for dedicated server prices like $100+ a month but if you look around there a pretty good deal. It's a small company and they are planning to add Terraria server hosting to there site.
https://simplehost.org/
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