Welcome.
George Gassaway's shuttle used a single composite motor in the external tank. The SRBs separate but do not contain motors at all- even with small motors in there he was concerned about the asymetric thrust issue. He also used mini motors in the orbiter but fired them after ET sep. to simulate an OMS burn.
Judging by his experience and the fact he did not use the SRBs I think you have a very serious challenge on your hands. This is not to discourage you - just to let you know what you are up against.
Check out his site:
https://members.aol.com/narshuttle/shuttlehome.htm
Personally, I would look at starting in a simple(ish) manner. Don't bother with the orbiter, or even the shuttle stack, at all - Not knowing what your past experience is but develop the project in an incremental manner - something like:
1) Basic single motor kits
2) Own designs - learn about stability and thrust to weight ratios
3) Cluster motors near to the center line of the model, again a basic 'normal' style rocket
4) 2 motor cluster with the motors well separated, perhaps so it looks a little like a very streched ET + SRBs
5) Back to single motors but an asymetric model design - now it is getting to be shuttle like but with a single motor in the ET (Estes kit)
6) Add motors to the ET - still having the main thrust come from the ET
7) No motor in the ET - now it is a boilerplate for the shuttle full stack
8) Full scale model.
Before moving on to the next stage make sure you solve all the problems with the current one. I know it is slow but NASA didn't start with the shuttle - they had enough problems flying single motor rockets at first
Personally, and living in the UK, I would use quickmatch for clustering black powder motors. I use this all the time and it is very reliable with motors starting at the same time. I know other modellers who use multiple Estes igniters and have no problems with that. Either way can work well with practice. It seems that US modellers tend to prefer multiple igniters, UK modellers single igniters and fusing.
Anyway you look at it is a big undertaking. Short model, asymetric model, clustering, widely spaced motors ....
On something like this the journey is going to be more interesting than the final goal, and I am sure extremely frustrating with many problems to solve on the way.
Personally I am at about stage 4, but then I am not after building a shuttle - just a conventional model with SRBs. I like interesting projects with plenty of complexity, and certainly a shuttle will give you LOTS of that!!!
Good luck with the project and keep us all posted on how you progress.