I've been able to get my schedule so that I go to the gym three times a week for the past two months. I've gotten some experience working out mostly with dumbells. I feel like I've gotten a but stronger, but I don't know if I'm really making progress fast as I should be. How should I be programming and planning my workouts for long term improvement? What resources are there for learning new exercises and building a plan that evenly works various muscle groups? I have access to a personal trainer at a reasonable price and I want to take advantage of that, but I don't think it's financially sustainable long term.
Start a linear progression like Stronglifts 5x5, do it till you start plateauing, then switch to something more advanced.
The best use of the trainer is to help you get your form down on the basic lifts, because crappy form is one of the biggest obstacles to maximizing your gains.