If you can't do that, remember to tuck your elbows into your chest and stop breathing for the duration of the shot, as a start.
Sorry i have to disagree here, dont stop breathing because that introduces shake, its not natural for your lungs and the minor distress will cause involantary shake it can also make you snatch the shutter button more.
A better technique is almost exactly the same as firing a rifle, where, you take several regulated breathes to steady your breathing, particularly if you have been hiking or climing stairs mountains moving quickly to get into position.
Then you breathe out and about half way through exhaling you gently squeeze the shutter while you maintain the same rate of exhaling the air from your lungs keep the shutter depressed through the shot and past the completion of the shot as you finish breathing out (this is to maintain the discipline and avoid any movement too early) if you have burst mode enabled it will obviously spray off a bunch of shots.
Similarly look at standard rifle shooting stances, long lens shooting is the same as for standing, sitting and prone in this regard
totally agree with this - slow, regulated breathing is better than not breathing at all. If you do decide to go down that path, do remember to start breathing again though.
I jest, - Personally, I'd go with the zoom first. Primes are great, especially for studio shoots, but I find the versatility of the primes helps more often than not. Yes, you could use your natural zoom and walk up and down, but you can't walk all over the place all over the time.
If I was working in a limited space where I knew beforehand I'd only use one setting - a studio, or a very specific shoot, i'd go for the prime, but otherwise the zoom will be my first choice. Yes, primes will be sharper, but modern zooms have pretty good IQ as well - differences if you pixel peep, but otherwise, really negatable.
further - if you're shooting outdoor and using fill flash, with the lens stopped down, the faster primes lose one of their advantages...