Can I move directly from SQL Server SP1 to SP3 or do i need to install SP2 then go to SP3. I was assigned to upgrade my servers 2014 just to make sure I don't fall into problems
Yes, you can upgrade directly to Service Pack 3. Service packs are cumulative; SP3 contains everything in SP2 and SP1.
This has always been true for every version of SQL Server I’ve worked with, and I'm old. But for those needing to read this from MS documentation on their web site instead of peers answering questions here, here is one official source:
Service packs are cumulative. Each new service pack contains all the fixes that are in previous service packs, together with any new fixes. You do not have to install a previous service pack before you install the latest service pack.
You will need to upgrade to SP3 before applying any SP3 Cumulative Updates. The name is a little confusing but a cumulative update is only cumulative from the relevant service pack. SP2 CU1 can only be applied to SP2; it won’t install on RTM, SP1, SP3, etc.
This acronym definition page may have useful info too.