First, Let's start with this:
https://resolume.com/manual/_media/en/r ... upport.pdf
Secondly, will all of your outputs be used to blend together on one screen? From the looks of your post, the answer is probably yes.
If you need multiple outputs to blend together on 1 canvas, you will want all of your outputs to be sync'd, Otherwise you will get something nasty called "screen tearing", where one output lags behind another output.
Nvidia cards only allow for 4 physical outputs to be used.
AMD cards allow for 6 physical outputs to be used at once. **However** AMD doesn't play well with Resolume (or at least as good as Nvidia does...)
SLI or Crossfire doesn't give you any advantages in power or outputs so I wouldn't go that route.
Having multiple cards will give you more outputs, but I would personally recommend matching cards. So for an example use 2 GTX1080's or 2 GTX1060's rather than using 1 GTX1080 and 1 GTX1060
Nvidia's Geforce (GTX) series cards will not allow for onboard port syncing, but Nvidia's Quadro series cards will.
I personally am very interested in getting a few Quadro's to do some testing here in the shop to see how well a current gen Quadro compares to a GTX1060/1070 in performance. If I can find a Quadro card that can push 20+ layers at 1080p for under $1k, I'd be interested in using that since I can sync my outputs at the GPU level.
The last solution for sync'ing your outputs would be to use a Datapath or a MST. Datapath's are expensive but their quality is much better than your standard run of the mill MST. You can send a large resolution to the Datapath (and MST) and then have that broken up into multiple screens. The Datapath will automatically syn'c the outputs so there won't be any screen tearing.
Having a Nvidia Geforce (GTX) card sending out 2 outputs into 2 Datapaths will still put you back at the same problem. Half of your screens will be out of sync with the other half since the Geforece cards do not do any port sync'ing. So I would only recommend using a single Datapath with this setup. Datapath's come in many flavor's such as DVI, HDMI, DP, and SDI (my favorite).
Something else that was being discussed earlier this week was an AJA HA54K. It appears to be very similar to the SDI version of the Datapath for for a quarter of the price. I'm very interested to get my hands on one and try it out.
Hope this info will get you started down the right path.
And again, please check out the following page:
https://resolume.com/manual/_media/en/r ... upport.pdf
In regards to ram, you'll want 6-12GB of GPU memory (8 is a good number) CPU memory isn't as crucial, 16GB would probably be fine.
Check out the GTX1080ti card. For the money, it's a beast!