You have several times more features than data points, which means the problem is underdetermined. So, you can't use ordinary least squares. The common ways around this are to penalize the $l_1$ or $l_2$ norm of the weights (called lasso or ridge regression, respectively). Lasso will make your weights sparse. Unclear whether you'd want this, because it would mean that your predicted ratings depend only on a sparse subset of the actors. In either case, you'll have to perform a search for a good value of the regularization parameter.
When there are many data points, you can often get faster convergence by training on minibatches than running through the entire dataset. The reason is that many points are redundant, and updating after each minibatch allows more frequent weight updates. Minibatch training can also be faster than stochastic gradient descent (i.e. training on single examples) because the underlying numerical computation libraries can play more tricks to speed things up.
Your weight update rule will also affect convergence speed, and may also require hyperparameter tuning. For example, using gradient descent, you'll have to play with the learning rate, possibly adjusting it over time. More sophisticated update rules are also available. Note that your objective function is convex in the case of linear regression, so this makes life easier than a lot of the situations you'll find people trying to deal with in this literature.
In terms of hardware tricks, you can try running your computation on a GPU. You can also parallelize the hyperparameter search across different machines.