Hi,
Some of the points require a bit more than one line to answer, and I would strongly recommend getting expert skills involved, unless it's not production boxes and you are just upgrading for the sake of it.
I'll try help with a bit of questions of my own
You mention "IIS and MS SQL" - does this imply they will be " hosting " something like a public website? Reason I ask (not to sound negative) but your standard OS 2012 License, and SQL licensing is not adequate for public hosting. You need a different OS license, and a very expensive SQL license.
1. - Hardware recommendations:
I'm a fan of Dell hardware, they are simply to use, but more importantly their service on professional warranties are better than anybody. Just make sure you take out " pro support" - often changing a 3 year Next Business Day warranty to 3 Years PRO NBD is only a few rands more. If the applications are mission critical, take a 4 Hour to fix Pro Support (within 4 hours on site with you replacement part) - It is more $ though.
With regards to what hardware - there are many different options, all depends on what you are going to do on it - Running some virtualisation? (Vmware?) - only a single OS, or different ones? What about backups? If virtual, you would need some disk space to store backups (called snapshots) - and I can make recommendations of very good (and even free options) for virtual environments.
With regards to migration/upgrade - there is no upgrade path to 2012 from 2003 - so you would have to install your new OS, and manually move what you want over.
The rest of the questions cannot really be answered in more details without more info. As a short description what I would recommend:
1. Hardware: Something Like a Dell Poweredge 520 server (add 6 or 8 internal disks, Raid controller etc)
2. Software:
Use VMwares free esxi hypervisor - brilliant for small single sites, and allows you to run a few boxes on the same hardware. You can also use the trial version of vmware converter - this will allow you to "convert" the physical server and it's OS and all apps to a virtual copy - at least you have it on new hardware until you can migrate apps /websites - and you can also run the new OS on the same hardware in parallel. For Backups I would use something like Veeam. (free/very cheap for basic option)
Hope it helps!