Mor eprecise to Dwayne - you need a lot of CPU and a lot p f processing power.
Unless you fail, amazon is stupid - clouds are extremely cost negative when you run a lot for a long time. FOr exmample, I am odffereed a 1 rack unit hosting for about 100 usad including 10.000 gb traffic in a large chicago data center. Beat that with Amazon ;)
What I would go with is:
* A SuperMicro 4 rack unit case that holds 72 discs possibly on a dual socket motherboard and a GOOD Raid card. The case already will put you back around 2500 USD - all in all without discs you talk of likely 5000 USD.
* A SUperMicro Twin2 case. That is a u2 rack with 4 "slots" that take dual socket mobos each, allows yout to put 8 CPU sockets into 2U.
If you scale that up, I would skip the Twin and go with a Del M1000e blade server case - there are new super small dual socket blades coming out where you fit 32 of them into one center (64 sockets total) and you can get a blade center for a decent price refurbisehd (the center itself does very litle that can break).
Finding hosting is another thing - you need a LOT of power, most data centers can not handle that outside of multiople tacks (kudos for CME Group new Aurora that has 12.8kw per rack distribution IIRC - but then, this is not normal hosting). I Know of a couple of US ddata centers where modern computers DO NOT RUN (ralk of 60 watt powre allowanc eper rack unit - a joke, most decent CPU have more power requirements).
There is always the tera box concept. someone was putting a LOT of vertically mounted discs into a special rack case.
A lot depends on your growth patterns and estiamted space. THis is the wrong place to ask - serverfault.com has mre info, but your local IT guy should know. THis is why senior popeople are senios.
But beware of clouds, their cost side is RIICULOUS expnsive for long term use. I am a big fan of private clouds (i.e. you OWN the platform) running myself on the 8th (next server delivered) 144gb with 6 sockets ;) The cost side I have is a nice joke compared what it would take Amazon or AZure every month to pay for that.