It is a very Starting Strength type routine. For what it is, I think it is good. I would add a touch more volume in the higher rep ranges personally, but it is hard to go very wrong with the program you have here if Starting Strength is the type of thing you want to pursue.
My only real beef is 1 set of deadlift. If you are working up to a top set of 5, fine. If however you are only doing 1 total set of 5....you need more. like 4x8 or something.
I would add a 4th day of accessory work. No barbells, work your back with rows and your obliques. Something along the lines of 10 sets of back work, 3 sets of rear delts, and abs. Also I am a fan of doing rear delts in your warm up on all days, because it keeps your shoulders healthy and everyone skips them if they wait to do it at the end of a workout.
Truth is, there are a LOT of programs that will work. Not just one. The only way you figure out what works best for you is to run a program to completion--no excuses. Set a minimum time, like 12 weeks, and then NEVER stop a program until you have followed it to the letter for 12 weeks.
You could also make a variation of that rule where you never modify a program from its original form (allowing for injuries or not having a piece of gym equipment as exceptions) for 8 weeks. After that you would have enough information to see if the change you want to make on week 9 is beneficial or not.----Like here: since you say you are going to stick with it regardless, GOOD. Do it for 8-10 weeks, then consider adding the 4th day of back and abs. Then see if it helps or not.
The difficulty isnt that there is only 1 program that will work, its that hopping programs does not allow you to learn how to work WITH a program or understand its purpose or organization. You are right that self discipline must be asserted here, so good for deciding to stick with a program.
Excuse typos, on my phone.