Maggie's Farm

Unless you want to be an MMA fighter or a body guard I would advise against most "strength training". Excercise is good, even weight lifting and moderate strength training is good. But if you choose to "be all you can be" and pump iron till it hurts I can guarantee you two things: 1. an injury. You may not care, after all excercising and endorphins are habit forming and are their own reason for doing what you're doing. Or it may not be too serious an injury and you can workout around it. If you wait until you are in your 30's or later to suddenly decide to become a world class athelete the least you will end up with is plantar fasciitis. I'm not saying don't excercise what I'm saying is don't allow your feeling of wellbeing and general increase in strength drive you to push your body too far. Find a moderate level of excercise that is good and stay with it.
2. When you get older than about 65 every injury, every insult to your body in your midlife crisis of over excercise will come back to haunt you. I'm betting in addition to plantar fasciitis you will develop some degree of shoulder cuff injury and of course knee injuries. I will repeat it isn't "excercise" that is the problem it is increasing the weight or the pushing the envelope that does it.
My advice is excercise carefully and don't let yourself get caught up in the superman (woman) syndrome. Yes you probably could bench press 350 lbs if you worked at it but why? Yes you probably could run a marathon or a lot of marathons but why? Excercise moderately, build up to it slowly over months, stay with it consistently and resist the temptation to go all out.

I gave more specific advice but you replied in generalities as though it was meaningful.
I repeat; moderate strength trainng is good. But what many/most people will do once they begin feeling their oats is see just howmuch they can bench press, just how much they can squat, just how much they can clean and press. Big mistake. Your major muscle groups develop quickly giving you confidence your minor muscles aren't ready to support.
The trick to reducing injuries while strength training is moderation. Lighter weights and more reps will provide many of the same strength benefits with lower chance of injury. But in fact a better choice for 95% ofpeople who want to stay in condition is develop an excercise plan and stay with it. Resist that temptation to do more and break past records. Sure if you are a football lineman or an MMA fighter strength and muscle mass is everything but if your goal is lifetime health and conditioning a moderate excercise program is the answer. Something sustainable that will not likely cause injury. And that is the point. There are only two kinds of people who advocate heavy strength training: those who have been injured from it and those who haven't yet. Trying to convince the latter that excessive training is bad and moderate training is good is very difficult. You simply have to wait until they have experienced the reality before they will listen.
My advice would be no squats and if you feel you must do squats in yur routine then do half squats with light weights. Don't do chin-ups with your hands reversed or behind the neck chin-ups. Don't lift weights with a spotter; seems counter-intuitive but if you "need" a spotter you are lifting too much. Use high rep light weight rather than low rep greater weight to avoid injury. For Running: unless you are in training for the Olympics you should be able to carry on a converstaion while running.
My most controversial advice would be don't use a trainer. If you are a professional athelete a trainer may be needed but if you are simply trying to get into condition and develop a good program a trainer will push you too far too soon.
But my primary point was that most people are simply unaware that they are likely to get injured and soe of these injuries are lifetime injuries that you will deal with for the rest of your life. Most can be avoided. But here is the problem: None of the likely injuries will come on slowly giving you an opportunity to recognize you are pushing too hard. If you do develop plantar fasciitis one day you will feel fine the next day you are in pain and this will stay with you the rest of your life sometimes less pain sometimes greater pain. Then and only then will you understand and wonder why no one ever warned you about it. Every injury is different, some are worse than a plantar fasciitis injury in terms of pain and disability and some or less serious. Some can be alleviated and may not bother you for years.
Bottom line is take it for what it's worth. If you over do the excercise you increase your risk of injury. Recognize that human nature and yur trainer tend to push you beyond what you should be doing. And last a moderate and even light training routine can be very beneficial and greatly reduce the risk of injury.