First up, take your own bag shopping to avoid the store's bags.
Clothes generally don't provide too much of a problem, the plastic tags holding labels on are probably the biggest problem.
Rehome any clothes you’ve finished with to the op shop and maybe pick up a few bargins for yourself when there!
Tailor-made suits, shirts and clothing are often packaging free and hopefully result in high quality, long wearing clothing.
When shopping consider what will happen to your clothes at the end of their usability. Non-natural fibres won’t break down for hundreds of years. Consider buying organic cotton, and Fair Trade is always a good option.
Thanks to Jodee for writing; What do you do with clothes that aren't good enough to give away/sell eg. x-kindy clothes that would normally go in the bin (and you've got enough rags)? The Salvation Army stores (and probably others) have a rag bin that they put all the crappy clothes in. The Salvation Army still gets paid for these items so I see it as a win-win. No clothes in my bin and I'm helping out a worthy cause.