Team Foundation Server - What Process Template is for me?
Are you already using a software development process like scrum? If yes you can try this Team Process Template over here.
How large is your project team and the project? Microsoft has published one of it's internal Process Templates (MPT) over here. You can get some guidiance and inspiration from this template.
As tangurena mentioned. People use the standard templates, change the bug a bit and store some documents there. I would recommend to keep the process 'light' as well.
However the process template isn't all.
Here are some ideas what I would do (in your case):
Create some high order workitems (features/stories) which stakeholdes can create (constraints and TFS user groups are your friend). They can then access their requested features via the TFS Work Item Web Access. That way you don't need a CAL for them
Create some reports which show planned work accodring to releases.
Setup the build automation and create Reports (a.k.a. Release Notes) from your workitems according to the builds.
What were the biggest advantages and disadvantages you've encountered?
Imho the biggest disadvantage is that you start believing that the template is your silver bullet. It's not, it's your starting point. The TFS ecosystem offers you alot opportunities to create own bits of software that fit your needs. Just check out the TFS API.