I am looking at a barebones kit for my congregation to play videos and stream broadcasts and display them on a 1080P projector. Tiger direct has a bunch but I not sure what to pick. I see a ton of AMD kits but I have only built 2 and they were both just for net surfing. My budget is right around $300 and they want a small footprint so I may have to get another case and I am thinking micro, mini,itx or whatever form factor.
My biggest concerns are,
 
1. Is hdmi out on the board going to be enough to push 1080p 100 feet to a projector
2. What is the minimum AMD processor I should be looking for? (for Intel, I was thinking an I-5?)
3. Is 8 gigs overkill for ram for what I am doing?
Thanks for any help, I am trying to pull the trigger while the deals are still good.

agent8I am looking at a barebones kit for my congregation to play videos and stream broadcasts and display them on a 1080P projector ... 2. What is the minimum AMD processor I should be looking for? (for Intel, I was thinking an I-5?)

Can't really comment on the AMD side (historically I've always used them, but have gone over to Intel recently), but if you're just playing an HD video, a Pentium would do.  Modern CPUs are surprisingly pokey - I built my parents a PC based around an i3 4330 (3.5GHz dual core), which is overkill for home-office tasks - I've had it playing 8 1080p YouTube videos without going near 50% CPU usage.  Obviously, if you're streaming lots of videos at the same time, things will change a little.
 

agent83. Is 8 gigs overkill for ram for what I am doing?

Depends what OS you're putting on it, and how many things you'll have it doing simultaneously, but for the above situation 4GB might be enough (I have a Linux Mint VM configured on my work PC as a general purpose apache/dev sandbox - it uses 500MB or RAM at idle, and I've yet to see it go over ~1GB used).