Please forgive my ignorance as I am new to the Flat top world. I just received my Alexander Arms Beowulf upper. It is a flat top with picatinny rail. I am going to need to put some glass on this gun as I will be using it in low light conditions to hunt hogs. What kind of rings/mount will I need to attach the scope to this rig? I haven't decided on a scope either, any help is greatly appreciated.

Does your upper have the standard sight tower?  If you want to mount a regular variable magnification scope like 3x9, you should get a riser like ARMS #36 or #38, then you can get #22 rings to go with it.  At 3x you'll still see a tiny blur on the bottom but not at higher magnification.
If you have ACOGs, either Trjicon's TA51 or ARMS #19, #19S will do the job.
On my setup the scope sits too low, I see a lot of the front sight until I have a riser.
[img]www.imagestation.com/picture/sraid70/p7b3679c3bfa6dc9f6f3bb155f77dbde1/fba2a17d.jpg[/img]

No sight tower, picatinny rail topped reciever and sight block. Was thinking of mounting a fixed 6 power scope, or less

Would slap an aimpoint on her, but this offers no help with light gathering

If you're not gonna have a front sight, go with AMRS #36 and #22 rings, I had a similar setup with my M4gery using a Leupold VariX III 3-9.  Mouting the scope too low doesn't give a good cheekweld, most shooters complain about the scope mounted too high, rarely about it being too low.  I found this out when I tried to mount the SN4 directly on the receiver.  I get my ARMS stuff from Wes at [url]www.mstn.biz[/url], ordered it one night and got it the next day [beer]

$104 for a set of rings is a bit excessive, more than I would feel comfortable spending anyway. Those look to be quick release. I don't care if they are permanent. Will any weaver style rings work?

Weaver rails look the same but there are enough  minor differences that they should not be interchanged.  A Pic accessory will only fit a Weaver rail if you file down the rail, hardly an optimal option, you should stick with Pic accessories.  QD rings may not be necessary, and you can find plenty of el cheapo aluminum rings, good stuff usually costs money.

RRA and Armalite both make one-piece scope mounts that put the scope at the correct height, are very durable, and they do not cost too much.  The RRA in particular is rather inexpensive and has worked well on my ARs.

I've never seen the RRA, but that Armalite scope mount is great. Check it out.

Steve.