That is like the hardest part, way to go. I recommend doing a linear progression like Stronglifts 5x5. Basically, the best thing you can do is keep going and don't stop for any reason.

hell yeah :arm-R:

I got no ideas to help you, but hell yeah

Alongside strong lifts 5x5 and getting the personal trainer to check your form, one of the first things you should do is 20 push ups right now if you're reading this

Personally I think you should only use the personal trainer to check on your form and get a sense of the more advanced workouts. Then after that do it yourself since really all they do is just watch you to make sure you don’t hurt yourself

Secks. Lots and lots of it. You must commit secks as an act of revolutio during ur commute, in ur work. Secks at home. Utilize ur new found physical acumen to create secks.

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.

That's not the mental wall that's hard once you get to the gym regularly. Sleep and diet are hard to get consistently.

Good luck!

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.

Keep track of your exercises you. See what you are capable of this week and try to increase the reps or weight of that exercise next week. This is called progressive overload

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I said this in another thread but for progression, I use the method of progressive overload. You can mess around with the speeds, advance quicker when it really is easy and slower when it's hard, but this is what I'm doing now that I'm hitting weights that are getting a bit difficult. For dumbbels, I will do 3 sets of each workout. Let's say I start on curls at 35 pounds. I start by doing 3 sets of 8 reps, and each day I come back, I add one rep. So it would be like this

Curls: 35 -8, 35- 8, 35-8

Day 2: curls - 35 - 9, 35 - 8, 35-8

Day 3: 35 - 9, 35 - 9, 35- 8

I do this until I hit 3 sets of 12, then I start transitioning to the next weight. The transition looks like this

Day 1: 40-8, 35 -12, 35 - 12

Day 2: 40-8, 40- 8, 35 - 12

And so on.

As far as choosing workouts, I'll list mine off. I workout 6 days a week and split between 2 days.

Day 1: deadlift, bench, squat, rows

Day 2: curls, tricep push down, reverse fly, chest fly, shoulder press, shrugs, upright rows

You could probably drop Upright Rows and chest fly and get this all done in one day although it'll be a whole lot. Alternatively, you could do that but switch out squat and deadlift and alternate days

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.

If strength is what you want, the most important things are weight (what can you do 3 sets of 6 with?) and getting good sleep.

How should I be programming and planning my workouts for long term improvement?

Anything that gives muscles two days of rest and covers all the muscles you want to do will work. The three days a week plan you're doing is fine for that. If your workout is faltering because you're running out of energy (ie: you do better earlier in your workout even if you reorder your stuff) you may want to do more days and splitting muscle groups (commonly arms/legs or front/back).

What resources are there for [...] building a plan that evenly works various muscle groups?

The way I learned it is push/pull, one leg/two leg, bend/twist. It's fairly thorough; I've only ever been surprised by a weak muscle group once (one covered by side lunges). If you'd like to extend that, I'd make push/pull separate for chest and arms.

There are various other things not covered by this (forearms, calves, neck muscles) but they're largely vanity muscles. If you want vanity muscles that's cool too, but you'll need to ask about the specific ones you want.

I have access to a personal trainer at a reasonable price and I want to take advantage of that.

A personal trainer is a great resource for learning new exercises. You can ask for recommendations for a specific muscle group, or pick out exercises ahead of time and ask them how to do them well.

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Remember: basically nobody ever came back from the gym thinking "Dang, I regret working out today, I wish I'd just stayed home and rubbed one out instead." Getting there is the hardest part, and it gets easier if you focus on the fact that you'll basically never regret going and always enjoy how you feel after.