There are plenty of alpine starter kits before jumping on something as hefty as Rainier. Mount Adams, Saint Helens, Mount Hood, and many more. Learn to use an ice axe, read about crevasse rescue, practice knots, get into running, and do as many snow climbs as you can. Rainier was not handed to me, I was poor and did not have an alpine mentor. However that didn't stop me from making a genuine effort that brought me to the proper precautions and getting associated with the right people to learn how to climb. It was tough and I had to learn a lot of hard lessons before stepping foot on the mountain. But it paid off in the end and I was safer as a result.
If you go up without the proper training, you won't just be risking yours (and possibly others) lives, you will be stripping yourself of the opportunity to learn to climb. That reason alone is worth not taking short cuts. I understand what its like to be on a budget, more than most mountaineers ever will. You don't have to join a climbing club to learn how either (although for some this has been quite useful). For me it was building genuine friendships with people and doing everything I could to make their experience in the mountains better. Over time I was able to pay back their lessons by taking leads and helping them through sketchy terrain as well as other useful assistance in the mountains.
On the gear department often times people do carry up too much stuff. That being said you will want a good layer system up there because it does get really cold even during summer. A puffy, warm sleeping bag, and a hat are highly recommended. My two worst sun burns I've ever gotten were on Mount Rainier. Days later I had so much oils coming out of my face that it soaked my shirt! Both of those times I had facial protection, but wasn't using proper stuff (or timing). You don't want to be Darth Vader after getting off Rainier.