Is it just all the collective matter including dark matter and the gravitational pull from all matter to itself?
and this is exactly right. There is no "gravitational force" that is separate from matter. Matter is the origin of gravity (strictly speaking we would say it's the origin of spacetime curvature) and it's the distribution of matter in the universe that determines the overall curvature.
Your second question:
And the only thing stopping it is the increasing speed of expansion?
is a bit more subtle. The dynamics of the universe can be calculated using general relativity. Basically we feed in the distribution of matter, and Einstein's equation tells us how the universe evolves. Generally speaking Einstein's equation is very difficult to solve, but with a few simplifying assumptions we can get a solution called the FLRW metric. This tells us that if the density of matter is high the universe expands then contracts again, while if the matter density is low the universe expands forever. Our universe appears to be exactly between these two cases: we call this a flat universe.
You've probably heard of dark energy. This adds an extra repulsive force i.e. it makes the universe expand. If the matter density was high the dark energy would be overwhelmed and the universe would still contract. In a flat universe like ours the dark energy doesn't have much effect in the early evolution of the universe but the repulsion is starting to be significant about now.
I've given a rather hand-waving answer as I'm guessing you aren't too interested in the maths. If you want more detail search this site for "FLRW metric" or see the Wikipedia article on it.