@nreece suggested our StorageVPS. Delimiter's storage VPS are HDD based but NVMe accelerated. We run ZFS with the ZIL/Cache on the NVMe. The storage performance is great, but CPU isn't overly generous. They are optimised to get data to/from disk.
I would recommend you look at our Cloud Compute product. Its based on Cloudstack, highly distributed Ceph backend - HDD with NVMe fronting the disks. It uses Cloudstack's advanced networking so you have a router/firewall by default as well as internal networking should you want to have more than just the DB locally.
https://cc.delimiter.com/cart/cloud-resource-pool/
A 1TB Ceph disk with 1GB RAM, 1 CPU will cost you $20.40/month
I am not sure what DB you are running but even if boost that up to 4GB RAM, 2 CPUs, 1TB Disk that is $34.62/month
Dedicated cores on the CPUs, 10Gbps uplink. We have a variety of customers running MongoDB clusters, MySQL/MariaDB, Couchbase and so on. Internal networks lets you keep the cluster network private. Just punch through the firewall for the ports you need publicly accessible or even limit the source address to stop non-authorised users.
If you want to give it a test, then just mail me on sales@delimiter.com and I'll get you a 30 day trial.
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Another option could be a cheap dedicated - we have some Dual E5420, 16GB RAM, 1TB Disk or 2 x 500GB for $200/year