Crikey, what exactly are you going to host that chews through 1TB a day?
You can get a reasonable Dedicated Server to run that service, and you won't need to spend $2,500 a month. I've had previous experience with Hetzner.de for fairly-priced Dedicate Servers. For €324 , plus €199 set-up, you can have a Dell PowerEdge machine with 3TB HDD, Dual Xeon E5-2620 (8 cores x 2 hyper threading, x 2 processors = 32 theoretical cores), 128GB of RAM, and 50TB of Outgoing traffic per month - they don't count/measure Inbound traffic.
Assuming you're using this 50TB box for web services, stick a Cloudflare Business package on top of that for $200 a month - you've got a pretty unstoppable force, for much less than the $2,500 budget you quoted.
I might be talking absolute baloney, but it just goes to show you what's possible with so little.