An important consideration is what, if any, ticket creation and tracking tools you will need.
I work on a leveraged help desk (after-hours), and we support about 15 different (Large/Enterprise) clients here, each with their own special needs when it comes to creating and monitoring the incident tickets.
We use several different versions of both Remedy and Peregrine Service Center for this.
Also consider basic tasks related to MS Office, we do get a lot of calls from all clients with regards to "How do I do XXX in MS Outlook / Word / Excel / Powerpoint / Access / IE / Windows?".
This raises yet another concern....are you going to be break-fix support, or will you include user training. Even though we are "strictly" a break/fix desk and not a training desk, we usually try to assist with "best effort" when we can.
By Far MS Outlook issues top the list of MS related inquiries(PST's, OWA, creating accounts/profiles on different workstations, general usage), but also basic things (basic to an IT pro)like mapping drives in Windows, or file management and folder permissions, along with missing *.DLL's and installing printers.
Remember the "smart ones generally don't call the help desk, they know how to either fix it themselves or find a solution on the net, and implement it successfully".
At least when the more seasoned user's call it usually is a "legitimate" issue, both interesting and challenging, as opposed to just hand-holding. (but they both pay the bills!)
For more windows oriented ideas, try reviewing some online syllabus's (syllabi?) for MCDST, there are sure to be some things covered in the MCDST materials that you will run into which I have not mentioned.
That of course assumes you are not supporting a *Nix enviroment, or some other proprietary s/w.
Also VPN issues are big here(especially "after-hours"), network connectivity (both at work and at home), and Wifi is coming on strong these days.
Interestingly enough, for some clients we DO support one thing or another, but for other clients we DO NOT support the same thing.
I strongly suggest you spend some time to clearly define EXACTLY what is supported in (and out of) your environment. Do you support Wifi? Does this include in the home?
It also wouldn't hurt to consider alternatives to provide your client(s) in the cases where you do not support it. (IE: "I'm sorry, we do NOT support WiFi networks in the home, have you tried contacting the manufacturer of the router or your ISP"?) In other words, if you don't support it, you should be able to direct the client to whoever does.
Believe me, there is plenty of room for "grey areas" in conflicting policies, which can leave the support personnel frustrated between a rock and a hard place.
Case in point, for one client that has a fairly strict "do NOT support Wifi" policy, coupled with a fairly lenient after-hours
"VPN support" policy (iow- "best effort"), what then, do you do, with a caller who is trying to connect using VPN at a hotel that ONLY has Wifi available?
Another important process that should not be overlooked or underestimated is server outages.
These are usually the highest priority, will generate a lot of calls (typically), can have the greatest impact on the clients productivity, and involve the most "support streams & teams" in resolving.
On a smaller scale, how will you handle a user's PC that won't boot into windows.(hardware support).
I get the sense this is an in-house operation, in which case some sort of SLA is not a pre-requisite, but may be worth considering if only as a guideline on policy and procedure.
Also I have found lots of great insights within the Tech Republic site, so spend some time surfing around, and I'm sure you will also find some as well. (Happy Hunting!)
Hope this helps.