OVH

OVH is mostly known as a shared hosting provider, but they do offer affordable virtual private servers as well.
With 27 data centers worldwide, features like backups or networking tools and with a large list of virtual private server types and operating systems, OVH might be a good and solid solution for your business.

You can get started with OVH and test drive a VPS for just $3.35/month, it will allow you to get a feel related to their infrastructure.
When you are ready to move to a more powerful virtual private server, there are plenty other options available, their VPS Cloud plans can be used if you don't need much RAM while their VPS Cloud RAM will help applications that are more RAM intensive.

In order to keep these affordable prices, OVH's virtual private servers are unmanaged, this means they will offer you the VPS and it is up to you to configure and manage it during its lifetime.
MailWizz is a web based email marketing software, which means it will need to run in a web server, be it nginx or apache, it will need PHP programming language and either MySQL or MariaDB to store your data.
Installing all these can be difficult and error prone, if you don't have enough experience, we recommend you hire a system administrator to do all this for you.
When selecting a VPS size from OVH to get started with MailWizz, we recommend using a VPS with at least 2 VCPU and 4GB RAM, VPS Cloud 2 is a good choice to get started with OVH and MailWizz.