Best and fast(est): Pay someone who already knows how to do it to do it for you.
Second best and fastest: Copy everything off the old hard drives onto the new ones. You'll still have all the cruft of your existing setup, and you might have to jiggle a bunch of stuff, and it may not be possible if you don't have physical access to all the hardware, but it'll give you a fairly quick migration path (albeit with a fairly significant downtime).
If you're dead set doing this yourself, it's straightforward in the abstract:
- Provision a new server
- Install all the same software (or updated versions, as appropriate)
- Identify all configuration and data that needs to be migrated
- Plan a migration strategy
- Test the migration strategy
- Perform the migration
- Redirect all DNS entries to the new system
(There'll probably be a customer-facing maintenance window in there around "perform the migration")
The devil, of course, is in the details. Unfortunately, that detail depends a lot on exactly how everything was configured -- and long experience on this site tells me that asking every detail that's needed, getting the wrong information, needing to get clarification on many points, and then providing the next piece of advice, isn't going to end well for anyone -- you or the answerers.
So, I'd boil down your choices to two simple ones:
- Pay someone to do it for you
- Start doing it yourself, and when you have a very detailed, specific question that is capable of being answered without devolving into a 10,000 word "tell you how to do your job for you" marathon, ask it here. If you can't get to the point where you can ask one these questions, revert to choice 1.
I don't say this to sound harsh, I say it to save everyone a lot of frustration and irritation. These sorts of questions are hell to answer as they're impossible to get enough detail into to provide a satisfying close -- and, for that matter, they're far too specific to your setup to even be useful to anyone in the future.