I get the same from full out, pumping-every-last-muscle-fiber sprinting too. It's something about the all-encompassing physicality of it - the brain almost goes into an instinct mode and all you can focus on is going as fast as possible, there's no room for anything else. Talk about a perfect way to get your mind off something!
I think though, for me, the best thing to do is a reasonable distance run (5k +) with a full-out sprint finish. During the distance part you get to really chew over whatever it is that you have to think about or that's stressing you out - then the sprint finish gives you a kind of catharsis at the end where, as above, you forget all about everything else for a minute or so and just, push!
Afterwards you feel so great that everyday stresses just fall away. Very few things feel nicer than being able to just stop, breathe, and walk slowly after a 5k with a sprint finish!
Of course, it's different if you're constantly doing 1RMs, but I doubt your workout consists solely of that.
Off the top of my head I can't think of any other major exercises that require a spotter. Squats maybe? But for those you can just use a smith machine.
I used to only go to the gym when I had a friend to go with (this was back in college so it wasn't a huge pain). Starting to go by myself was the best change I ever made. Not being beholden to another's schedule for your own wellbeing is a glorious thing indeed.
With a smith machine, you don't get the full range of motion you have with real barbell squats - it's straight-line up and down. I also am not a fan of the twisting motion you need to perform to get the bar locked in.
Have also done a good amount of biking but haven't lived in an area that's safe for it in a while.
Or when you snowboard instead of a slalom you go just straight reaching 50-60 km/h with the board... Or after a big jump... (or when you understand that there's no place to go and you're gonna crash no matter what :-P ).
There are really, very few things that can be compared with a pure adrenaline rush.
I have the impression that there's' a trade-off between effectiveness and safety though, and this advice is pretty far towards the safe side of the spectrum.
And yes, I do have horrible technique. And since I don't have a personal trainer, no one is ever going to tell me when my technique slips, so I'd rather not rely on it.
The others where loading up machines with weights I could not have moved if it weren't for the fixed movement plane of the machine, that ultimately meant trouble for my lower back (leg press) and grinding in my knees (leg extensions).
I'd recommend doing the big 3, but starting off light. Focus on improving the movement. Record yourself, fix your form, develop awareness of your body position (for example - what does "butt tucked in" feel like?) and learn how to dump the bar if something goes wrong.
Above all: don't let your ego get in the way. There's a fine line between "just one more" and "one too many".
Barbell training is quite safe if you learn proper technique.
Also, if strength is a goal, it's very difficult to work with heavier weights without a bar.
Endorphins are often given as a reason for why exercise makes people feel better. But when you give people an endorphin blocker (so the endorphins can't have any effect) you still get reports that exercise helped those people.
There are about 12 possible plausible mechanisms of action for why exercise may help improve mood. Thermo-regulation is another that seems promising.
Could have something to do with the hormones and neurotransmitters that the body gets flooded with after lifting, could just be light-headed, could be something to do with all the tiny muscle tears...not entirely sure.
On the flip side, I'm a bigger guy(6'5"), and I just feel beat down and ache for days if I do any substantial distance running.
Sprinting though, seems to have similar physiological symptoms as lifting, and I believe several studies have shown that intensity rather than duration of exercise produces these effects.