What contributes more to bitcoin network? Using Bitcoin-Qt or running a miner? What would make a better support for bitcoin?
Does it really makes any difference to store blockchain locally instead on a remote server?
What do you mean contribute to Bitcoin? What is your goal?

If the goal is to help with the propagation of nodes, then setting up a bitcoin-qt on a server is nice for the infrastructure and probably the best for a long-term, good guy greg operation. Become a trusted node, add to the infrastructure. 

Coins are mined at a steady pace. There's no threat of them being disrupted or mining operations to discontinue. If anything there's a growing number of miners and the difficulty rate is adjusting to match that. 

The best thing you can do for Bitcoin is to continue to use it (marketing), or apply one of your skills to its community (entrepreneurial, development, marketing, design, or other). Make a cool Bitcoin t-shirt (and sell them), buy something using Bitcoin, sell something using Bitcoin. When you encounter something difficult in your use of Bitcoin, make suggestions on how it could be improved. People will listen. Your opinion is valuable and matters.