In res, we're human. In ANY airline reservation office you will see the agents who couldn't care less. On the other hand if you consistently offer the best customer service you know how to, and treat each customer as an individual you will find your job rewarding. I know I do.
As for the sales push, I know the feeling. If someone is just looking, they'll say no, but if your service and price has won them over you'd be surprised how many people simply say yes, let's do it.
I don't know how BA operates, but US carriers are required to give abbreviated fare rules (min/max stay, refundable/nonref, day/time/blackout, change penalties, tkt time limits, etc.), and Codeshare/OAL information. That is simply good customer service, make them know what they're buying.
I wish you the best of luck, and have fun, you're just a person getting paid to talk on a phone. On the other end of the line is a person as well.