dedicated server = yours, you can do with it what you want and you are not limitted (except by the hardware and your own configuration skills). More powerfull than a slot server as you get all the server specs just for yourself. Expensive.
slot server = Limitted. Good if you do not want to hassle with settings and/or configure a server yourself. The host sets things up and your start playing. You depend on the settings the host set your server to though. Cheap.
If you never managed a server and do not have anyone close to you who can do it for you (and actually knows what he is doing) just go for a slot server. That way you can start playing as soon as possible.
Just do not buy it for many months, even when they give you a cheaper price. First go for the full monthly price, see if you like it and if after a few months of use you are sure this is what you want/need buy it for a longer period (cheaper).
If you do not like the server you can just cancell it and not stuck to it for xx months.
Read the terms of service before buying!! Many server hosts have weird rules so better know what those rules are!