Don't look at your choices as #1, #2 and #3 (i.e. #1 is your favourite, and you'd consider doing #3). You have be as willing to do job #3 as you are doing job #1. The selections for occupations are not staggered; the selections are grouped (i.e. ROTP selections happen together, DEO selections happen together, and NCM selections happen together).
How the selection happens though is that with your score (CFAT, TSD, Interview) in occupation #1 you might be listed as the 60th person; in occupation #2 (same score but different trade) you're 89th; and occupation #3 (same score different trade) you're the 10th. In that case you're going to be selected for trade #3 as you're best suited for that occupation according to your score and the other individuals applying for that occupation. So yes your name will show up on all 3 lists, but you'll be selected for the one you're scored highest in.
It's hard to tell you online what your chances are. It depends what your education is, how you score on the CFAT/TSD, how you do on the interview. Getting into the CAF is a competitive process. For the most part if you're only spending a "few minutes of time" in a CFRC and you have a university degree the recruiter will speak with you about applying as an Officer. However at the end of the day you need to select an occupation that you're going to enjoy; so if you think you'll enjoy being an Int Op that's what you should be putting on your application.