The machines have been addressed, but what about the user? Since you are new to the detecting game, let me throw in some other variables. The 3 machines you mention are all above average in weight and arguably learning curve. Can you physically manage a heavier detector? Can you spend enough time using it to learn it sufficiently? Are you technically inclined enough to be patient enough to learn the ins and outs of these machines? Actually they all can do fairly well as turn on and go at first and get the finesse later (some more than others). A PI can be frustrating though simple to learn. The CTX can be overwhelming (it has so many options and display info). The Excal is tone driven and takes getting used to (though it could not be easier to set and go beach hunt).
You just now mentioned the Deus, its a great machine and by far the lightest/easiest to swing. But it is not great in the salt sand or surf IMO. Can do park and prospecting with the understanding that multiuse means compromise and obviously no machine is the best choice for each of the three kinds of hunting.