I compete in both amateur and Pro/Am events, so I have some experience in these matters and can give you a straight answer without bashing either form of competition.
Okay, now for the pros and cons of each.
Pro/AM
+ You already have a teacher to be your partner.
+ Your teacher is highly skilled, so all the training focusses on you, the complete individual attention will help you progress.
+ You already know you like your teacher as a dancer and a person.
- Pro/Am is VERY expensive when compared to Amateur competition. At a local Pro/Am comp I will spend well over $500 in entry fees and fees to my teacher to pay him for dancing with me in one style. At the same comp, if I danced in one style of Amateur events, I would only pay $93.
- Pro/Am doesn't get a lot of respect from some of the amateur dancers who have never done Pro/Am.
- Sometimes it can get a little complex planning what events to enter because you have to take your teacher's other students and Professional partner into account.
Amateur
+ You are dancing with a peer rather than a teacher, so the partnership dynamic is different; it's more of a team
+ There are many opportunties for low-cost competitions. For example, the local ballroom club I belong to hosts amateur competitions that cost $15 per person for "all you can dance."
+ Ongoing expenses are much lower because you and your partner split the cost of lessons and because you do not have to pay for extra lessons to get extra practice time. If I wanted to dance with my teacher 5 days a week, it would cost me $350. If I wanted to dance with an amateur partner 5 days a week, we'd split one lesson and then practice four additional days at a cost of $55.
+ Some of the best coaches don't teach single students or Pro/Am couples. As an amateur couple, even a low-level one, you'll have access to a greater variety of coaches.
+ More flexibility on deciding which competitions and events to dance in.
- Finding an appropriate partner can be DIFFICULT. It's the most difficult thing in dancesport, in my opinion.
- Since your partner is another amateur, you would have to work around their work, family, and social schedule. Synching up schedules is not always easy. In fact, scheduling compatibility is a prerequisite for a satisfying partnership.
In general, Pro/Am is easier to get started in, but harder to maintain over time -- mainly due to cost and scheduling issues. Amateur presents the hurdle of finding a partner, but once you've got that handled it provides you more opportunities at a greatly reduced cost.
I started in Pro/Am and keep doing it because I really like dancing with my teacher. We've been working together for a number of years now, I do it simply because I enjoy it. I've also had a series of Amateur partners, and I find Amateur dancing more satisfying in the end because it's two peers working together as a team, it is more prestigious (even on the lowest levels), and because of the lower expense. Another reason why I've stayed with my teacher all this time is because Amateur partners come and go but my teacher is constant. It's nice to know he's always there for me, it cushions the blow when amatuer partnerships break up. My Standard partner and I haven't been able to dance together for nearly 10 months now because he needed knee surgery, and doing Pro/Am with my teacher kept me busy working on my own dancing while he was out. It has also given me a chance to explore another style that my partner wasn't particularly interested in.
If you can afford the time and money to do both for a while, then that's the best of everything. If not, then I suggest dancing in Pro/Am events with your teacher while you look for an amateur partner. Once you start working with another amateur, you'll eventually come to a point when you'll know you don't want to do Pro/Am any more.