For all of those profiles and elevation data, I suspect you’d need 256GB of RAM. I only use one profile myself (foot) and just about get away with 64GB, so can’t say for sure though. The number of requests shouldn’t be an issue on a reasonably spec’d server.
Can I assume you also don’t want any downtime whilst you reprocess the latest OSM data? If so, then you’ll likely need a second server of the same specification, and you’d run them in an A/B fashion. So in January you’d serve all traffic from server A, and on server B you’d process the latest OSM data. Then in February you’d flip traffic to be served from server B, and do OSM processing on server A. And so on. This way you achieve zero downtime.
All of this comes with some administrative cost/burden though. So if you have no experience with setting up and administering servers, you’ll need someone to help out with this for sure.
Regarding the server itself: Definitely use a bare metal server. You could either buy one (there’s plenty of second hand options with lots of RAM - RAM is key - on ebay), or you can rent them. If you want to rent a bare metal server (referred to as a “dedicated server” in the hosting world) then you should look at places like Hetzner, OVH, Leaseweb for reasonable prices on large amounts of RAM. Another good one is Heymman (Heymman Servers) but they rarely have stock. It goes without saying, but avoid AWS/GCP/Azure/Linode/DigitalOcean for this - you will pay a fortune for the amount of RAM you require.
Hope this helps,