Hmmm... OK, Rainier is a fun hike, unless you go via Camp Hazard or unauthorized Willis Wall.
Now, first do you want to rush up or nice easy venture and have fun?
RMI can rush you then drop you if you are not prepared. That's money out the door.
Do you want to get in shape? Remember you do not run up a mountain, it is one rest step at a time.
Now, here's a suggestion from someone who has spend 40 years hiking/climbing all over the place.
My favorite work out is Mt Si, fine a comfortable pack [internal frame].
Save yourself 4-8 plastic 1 gallon milk containers including lids. Start with 1-2, just to gain your strength. As you feel comfortable with that weight add 1 more.
Do Mt Si once a week but during the week go for a walk every day with the same weight as what you are going to do Mt Si. No less than 2 hours.
Now this may sound crazy but you can do it. Keep this up until you can do all the containers up Mt Si to the Haystack and back to Parking lot in 2 hours 30 minutes. Yes, you read that correctly.
WAIT DON'T PANIC!! You empty the containers at the top!
Yes, you can just push yourself. No Pain, No Gain! Just keep telling yourself you can do it.
Do Not Cheat, do your work out everyday even if it is pouring outside or the weather is beautiful.
Good luck on your adventure, you will enjoy it if you are in shape and ready. Find a class such as Mountaineers course to understand safety and the in & out of self arrest.
Go out now and learn to be in the cold. Turn that car heater off so you acclimate yourself to the cold, once your step outside it will not feel cold to you.
MtnMutt