Pretty much. Use weight that you can still have good form with and train until failure.
For shoulders, overhead press is king. Standing with a barbell, or sitting with dumbells I go to.
Kade's got it right ... OHP for shoulders. Hamstrings - deadlift. Proper form is imperative
As for what to do (more reps, weight)... depends on what you're training for. Strength? Size? Power? Different techniques provide different results. Bottom line, you want to see progressive overload (this guy gets pretty science-y, but it's very good information). Whether that's more reps, more weight, more sets, decreased rest periods, more intensity... just push yourself to do more.
Also, I was *so* envious of your cage, I reogranized my storage/furnace/workout room, to make room for this bad boy.
Now I just need to get some plates and a bar. But (I suppose unsurprisingly) every fitness outlet I looked up, plates are on backorder.
I've added Overhead Press to the regular workout, but have decided against a Deadlift as the gym is on the second floor. I know I could theoretically be as safe as possible, but just don't want to chance slamming on the floor too much.
As for what I'm training for, goals 1, 2, and 3 are to get exercise at home in an attempt to get weight down and increase overall health. After that strength is 10x more important than size/looks.
I watched a little of the videos, will do more as I need to explore new techniques and form more.
The cage was actually a great deal on amazon, got that and the bench for $380 shipped. I assume you are already committed to what you got, but if you want the link for mine hmu on facebook. Mine also has mounting for an optional lat-pulldown attachment. If I do well and keep with my routine I plan to reward myself with that in a month or three to further expand what I can do.
And yeah, finding weights was an absolute bitch. Found a set I liked (300lb set from Dick's), sells for $250 new and people were selling the set on facebook for $500 and getting it. I actually planned a 90 mile each way trip on my day off Friday to pick up a set far away, but that very morning my local store got a shipment in which I quickly gobbled up. They had 10 and were all gone in 90 minutes.
Played with things today and here is what I've updated the routine to:
3x10 Bench press @ 90lbs (30ea)
3x10 Sit-ups.
3x10 Curls @ 60lbs (15ea)
3x10 Squats @ 130lbs (50ea)
3x10 Overhead press @ 70lbs (20ea)
3x5 Inverted row.
I can add a little weight to the bench or overhead press, depending on if I'm doing the list top to bottom or the opposite. Curls absolutely kill me. And even though I've upped the squat weight a lot I think I can still push that higher.