As a 22 year old former college football and track player who is suffering from previous injuries, including a fairly severe back injury, I would advise that unless you are going to seriously compete in athletic events, I would stay away from very heavy lifts even if you didn't previously get injured.
What I have learned over my 16 years of athletics and 11 years of heavy power lifting (heavy being relative one's level of strength) is that injury is inevitable. You will get hurt at some point if you are athletically competing and you will get hurt at some point if you are heavy lifting.
If you are trying to bulk up and get as strong as you can then you need to lift heavily to push yourself into progressive gains, but I would ask yourself if bulking up and getting as strong as you can is worth the greatly increased risk of injury you are putting yourself through. And as a distance runner there is no need to bulk up, and it would actually be a hinderance to your running.
Yes squats and deadlifts are great lifts for your back, hips, hamstrings, glutes and quads. All of which are more important areas to exercise than your pecs, delts, biceps, or triceps. I would strongly advise that you, particularly considering your past injury, focus your workouts on your lower body because you need to re-strengthen your hammies, quads, hips, and lower back. I would venture to bet that you have lost significant strength and flexibility in those areas. But I guarantee that low weight, highly dynamic, mobility focused lower body exercises like single leg squats, front squats, single leg romanian deadlifts, and bosu ball squats, basically any lower body lift that strongly engages stability and core muscles, would give you better bennifit at a much lower risk of injury than would heavy squats or deadlifts.
As for if a 300 lb squat or deadlift is good or bad for someone to do, it is really a mislead question because someone's ability to lift a specific amount of weight is arbitrary. It is all relative when it comes to strength. 300 lb's to a 5'6" swimmer would mean a very different thing that it would to a 6' former football player and it would be different to a 6' distance runner as well. What I would suggest to you is not to look for a specific weight. Lift what you can while still feeling confident in your stability and control. Push yourself, but do it at a low enough weight that you don't feel like you are risking your health in any way.
As for myself, my max squat while I was a player was 415 lbs, but I don't try to lift anything over 225 lbs any more. I rarely even go above 40 lb dumbbells or kettlebells anymore. I don't feel like I have any reason to increase my chance of injury now that I am not seriously competing. So I stick to low weight, highly dynamic, mobility focused exercises with the purpose of increasing my effective range of motion and my muscular and cardiovascular endurance rather than increasing my max strength.
So you need to make the same decision for yourself. It is all about cost benefit analysis. I doubt that you would benefit more from increasing your squat max to 300 lbs than you would for increasing your flexibility, stability and core strength (aka. effective range of motion).
Yes deadlifts and squats are good exercises for you to do, particularly considering your injury, but don't try for some arbitrary number of pounds. Do what you can while feeling confident in your ability to stay safe during the duration of the exercise.