The fact that one moment you are considering trying to go DIY on Digital Ocean as a complete amateur with no sysadmin experience and the next you are looking at WPengine who are a top end managed solution suggests you are out of your depth. Imagine if this was some other area of business, say you were going to open a bar and you were one moment going to hold a "decorating party" with your friends and the next you were looking at flashy commercial interior design companies. It would be difficult to take someone seriously if they had so little clue what they wanted.
Ideally whoever has designed your site should be able to make some recommendations. Any professional web designer will have bought hoisting before and likely have a few companies they trust. Your designer will also have a good understanding of your business model and what you are trying to achieve so in a good position to estimate the expected traffic. Finally they will know your site and how "heavy" it is likely to be on the server, one Wordpress site could be orders of magnitude more efficient than another depending on how it has been designed.
If your designer can't recommend anyone then just speak to a reputable host, choose one that offers the full range of services. A decent host will be able to move you between packages and hosting sites very quickly I would start small and trust the host to be able adjust to your needs. A single wordpress site is hardly exotic.
If you really think you will need to scale quickly, and want to do it yourself to save money then go for Amazon web services. You can configure it to autoscale from a free tier micro instance auto add load balanced balanced infrastructure right up to as big as it gets. There are guides online how to do this but you need to be careful (eg a botnet tries to brute force your login page and you scale up, costs you money and helps them hack you). Something to consider is that I think wpengine use Amazon behind the scenes, the premium they charge is effectively to manage that for you and many people consider that money well spent.