You need hosting recommendations WordPress (normal + developer) managed.

For that kind of budget, you can quit the job of system administrator, but the web will not be as reliable.

$ 6: You can get Digital Ocean or a similar service: 25 GB SSD VPS, 1 GB of RAM and data transfer / month with dedicated IP, including backup.
$ 6: For server maintenance (using a technical support service and a monitoring system)
$ 5: For wordpress maintenance (that is, a wp administrator add-on, a wp backup system, monitoring and security complements). However, no one can guarantee that all add-ons will work well.
That's $ 17 per month

The speed should be fine if you choose a VPS data center close to your target audience.

However, it will not be reliable, since:
– Support, includes server and wordpress monitoring system. At that speed, the help desk can restore the backup from the backup of the previous day, but that will cause the loss of data in the middle. The cost of recovering data during a problem is too high.

– You depend on a single VPS, which is risky. Even DigitalOcean has experience in the damage server. The sysadmin service can only be restored if it happens, it can not guarantee the uptime of your wp site. For this, you need a second server and a loadballancer server, so that when one server is inactive, the second server could take over. The second server must be located in a different city to minimize the risk. That would be more than double the budget.

– It is known that WordPress add-ons cause problems, even woocommerce. Next month and next year, some say WordPress will be out of service for its new but disturbing Gutenberg editor. For the sysadmin service that WordPress maintains, including the analysis of each of the add-ons, the cost will be much higher, especially for this new Gutenberg era.