On the personal trainer issue: just remember, they work for you. If you tell them what your goals are, they should be willing to help you reach them, and if they're not supportive or accepting, fire them and get another - it's that simple.
If your chest shows, your chest shows - don't let self-consciousness sabotage your workouts. The 350-pound guy sweating away on the treadmill in the corner is self-conscious too. Hell, even the ripped guy doing perfect bicep curls in the mirror is probably insecure about something (probably whether or not the other guys in the gym can tell that he's gay). They're all too self-absorbed with their own body/appearance issues to care much about yours.
In general, it's probably a good idea to out yourself to your trainer if you're not on T, because they need to know that your muscle growth will go slower and they can't increase your weights as fast. Also, your strength will develop in a different pattern - you might increase pretty quickly on leg and core strength, and even develop some pretty solid arm strength, but pullups and shoulder stuff will be a struggle for you and you'll need to start much slower than your weight and strength in other areas might suggest. But make sure they know you're trans and want to bulk up, not just "tone", so they don't keep you on the little baby weights forever.
If you are on T, the above doesn't apply. But if this is your first time training since starting T, you might want to emphasize that you want to use free weights and bodyweight exercises (as opposed to machines) as much as possible - machines aren't as good for developing the stabilizing muscles you need for your strength to be useful in real life. In fact, you might want to bring this up even if you're not on T. But it's a particularly big deal if your body is reacting as a male body, because targeted muscles will bulk up fast as hell on machines but the related groups (as well as your coordination and balance) won't keep up.
