My goals aren't the same as yours but some of what I would have done differently apply to you as well.
First, I would follow the program 100% if your goal is what the program's goal is. My first "real" program was rippetoe and my biggest mistake was starting out right away with heavy weight. I've no idea how come I never got injured back then, especially on the deadlift and I do now but I so should have listened.
Should have started with just the bar or ~100 pounds on deadlift and squats.
Should have done mobility/stretching/foam rolling(didn't even know about foam rolling until years after I started) an hour daily .
Should have learned the technique properly. Get videos and upload them on youtube and make a forum post if you need someone to check it out. Take the video from the side. I should have kept the weight at ~90% or less of the 5rm max(since I was doing rippetoe which asks for 5 reps) until I had near perfect technique. It's not that hard to learn it if you have someone to show it to you and you have the flexibility for it.
I would have learned about sleeping 8-10 hours everyday , I would have learned a lot about food AND HOW TO COOK if you don't have someone to do it for you. I would have eaten cleaner and way more vegetables(main reason I didn't was that I was lazy to cook them but now that I do I found a way to cook for ~1hour per week and have veggies throughout the whole week)
I would learn about contrast showers, using ice, warm baths and cold baths.
I would learn about supplements. the trick with supplements is that they should be what the name says. SUPPLEMENTS. If you are getting 50grams of protein a day, then obviously investing in a protein whey will benefit you a lot more than if you were already eating 300grams per day. If you are having pains on your knees getting some fish oil and some glucosamine chondroitin MSM (or whatever they are called) and possibly vitamin C will help. If you are lacking energy throughout your workout maybe getting some caffeine supplement will help. If you can't sleep properly get a better bed and some supplement that helps with sleep
Just make sure that you FIRST get a good consistent diet and 8-10 hours of sleep before you start adding supplements.
And lastly I would be a LOT more careful about injuries. This is a problem though with beginners as things at the start are SO hectic and you get so much information that you have no idea what to do and why so for some it might be being less "careful" about injuries for some it should be more careful.
In general until you learn your body better, if it hurts and its not muscle soreness or lactic acid or whatever(I haven't done more than 6 reps in a long time ) then you should start worrying a bit. If its muscle soreness you better be lifting.
The rest of what I would change really only relate to olympic lifting so I won't mention them unless you want me to.