If I look on Nice Servers: Nice Servers.com it will have the option of buying a vanilla server or a 'Modded' server, can I buy the vanilla one and mod it or do I have to get the modded one to be able to have a mod on the server?
It always depends on what the host provides. The difference between "vanilla" and "modded" server is that modded server uses Forge jar, but vanilla server uses only original server jar. Forge has also original server jar file, but the thing is that servers are normally setupped so they start one particular JAR file, by NAME. (when server starts, it calls one given name in the start command) But usually you can rename any server jar to get it called, when you alter it for another one.
If the host provides FTP access, you still can change it to whatever you want (spigot, forge, bukkit, vanilla..... ). There is normally no other difference between those servers, except that modded servers might be more expensive, but can have allowed higher hardware limits, because they do need more RAM and so, so it is reasonable to give them more that way.
BUT it fully depends on what that particular host provides. You should go and ask their tech support, to get detailed information, because this varies from host to host.
IF you want mods on your server, you need modded version. If host provides you preinstalled setup, you as a begginer might want to get advantage from that.