Hi Aidian,
My training for Rainier has been running, like 6 miles in hilly areas twice a week, and hiking places like Mt Si (try to get to 1:15-1:20 without haystack), tiger cable trail 35 min, or Mailbox 2hrs. Like Phil said don't pack too much weight, just a few essentials on these hikes. Try the heavy pack to Muir once, or even better climb Mt Baker on the Easton or Colman-Deming. Doing this shows you what works and what doesn't work, and it's easier than Rainier.
I've climbed Rainier quite a few times with quite a few people and the most successful seem to be distance runners mentally when it comes to first timers.
There have been some studies showing Ginko Bibola helps some with altitude, and on the fluids, try mixing Gatorade or Poweraid, this keeps you hydrated and the electrolytes up high. I only take a MSR XGk with a large pot for melting snow, and earplugs, believe me it helps with tent flap noise, and other people making noise at base camp.
Bill