You will need at least one Cent OS 6 (64 bit recommended) VPS/Dedicated server with nothing else running/installed. If you would like to run checks from multiple locations you can setup additonal check servers at multiple data centers. Each check server can also be a part of the MongoDB replica set which allows the database to automatically failover if one of the check servers running MongoDB goes offline. This helps to ensure your users checks will always run. In order for the MongoDB automatic failover system to work properly, you always need an odd number of MongoDB servers. If you want to run an even number of MongoDB servers you will need to run an additional small server to run an arbiter which doesn't store any data and is simply used to help vote for a new primary if the current primary goes offline. The arbiter server doesn't require much resouces so you could install it on your current WHMCS server or another server that is used for something else.
On your WHMCS server you will need to install the mongo driver which can be easilly installed using pecl. You will also need to be running at least WHMCS 5.0.3 and using the new default template or a variation of it which uses the same bootstrap CSS. You can also edit the included template files to fit your theme.