To OP
You are looking for a server to only start email marketing campaign....You are kidding
It is an outdated method of marketing. Anyway, this is just my personal point of view so don't take it so seriously.
In my opinion, you should contact reliable and well reputable web hosts thorough Live chat and ask outgoing email limitation. If you opt dedicated server for email marketing campaign, then definitely you will get more privileges, but if you are not able to afford dedicated server, then you can go with vps as well. However, to avoid IP block issues don't send emails in bulk; split them in groups and send after specific time of span, hence your IP won't be get listed as spam