Depends on what you are most comfortable administrating, really. You run a mostly Windows environment, so my first suggestion is to go with Windows, and your primary "ugh" factor with Windows is the cost. Big downside, but that's the cost of using Windows in a mostly Windows environment.
If you like and are comfortable with Linux, go with that. The main drawback is that while most of what you labeled are relatively simple and almost painless to do with it, some of it could be a pain, like contact syncing. You may have to dive into LDAP and such in order to accomplish it, and Linux extracts a pound of flesh for the learning curve where with Windows you'll need to pay in cash. On the upside, you get a wonderful education on how things work while becoming intimately intertwined with the business so it may be a source of job security :-)
Linux does offer a lot of flexibility, and there's almost surely a way to get it to do whatever you want it to do and more and it's free (monetarily) while expensive in learning curve for some technologies.
For what you named I think the biggest headache for me would be the calendaring and contact sharing. There's a groupware solution that may work for you on Linux...so...I'd say go Linux, and if you can't get it to work transition to Windows.
Server specs...minimum 4 gig RAM, a couple drives for RAID (small business...with some budget I'd get hardware RAID mirroring), drive size depends entirely on your needs (you didn't say what the business is and how much data you're pushing), good gigabit network card and switch. Depending on your expected load on the system you may want to look at either RAID 1 (mirror) or RAID 10. Avoid RAID 5 with high capacity drives. That's asking for issues. Backing up can be either to a decent tape drive or, again depending on budget and file sizes you're expecting, external hard disks of high capacity. Tapes last longer but drives are pretty fast and the interface for Firewire/USB/SATA/etc. aren't going away anytime soon, while some of our older tape technologies aren't the easiest to recover from once for some reason the drives are replaced or updated. For a small business using large capacity hard disks as a backup medium isn't ridiculous, given pricing on external terabyte hard disks. Depends on what your backup cycle is expected to be and how long you want to keep old data.