Bike position is important in comfort, and if you're not racing you certainly don't need to be in an agressive position, but core body strength is also crucial to comfort on the bike. The best thing you can do in the weight room is make sure to exersize your lower back (back extensions, seated row), abs, obliques, and upper back.

As far as speed, the best thing you can do to make yourself faster is to do speed intervals on the bike. Strength is important, and you can work your quads, hamstrings and calves in the weightroom, but the most effective way to get faster is to make yourself ride faster. There are many ways to do intervals. Start with short 15-20 seconds all out, with 30-60 sec rest. Start with 3 to 5 of those. If that doesn't feel hard enough, then extend the time "on". You will always want to make sure you are recovered before starting the next interval, so increase your rest time between intervals as you lengthen the speed part as well. You can practice doing pyramid intervals too. Play around with it and see what works for you. I'm no expert, but those are my 2 cents.