Greenhorn, where do you live and when is your trip? Here are a couple of tips from me if you want to be successful and have fun on your climb.
Sounds like money is not an issue to you, so I'd go and buy mountaineering boots for the climb, instead of renting them from RMI. Get the new leather ones like Sportiva Nepals or Scarpa Phantoms, not the double-plastic ones. Go hike in them and break them in. Good boots make a huge difference and light-weight pair will keep you happy on the Paradise to Camp Muir hike (and you don't have to bring 2 pairs of boots like many do).
Secondly, if you can, rent crampons, if not, buy a pair online (10-point crampons are good enough), there are sales going on right now or you maybe able to get a pair of used ones. Yes, even if you don't have snow where you are, fit them to your boots and try walking in them. It's very awkward in the beginning. Make sure to wear gaitors when you do or wear a skinny pair of pants that you don't mind trashing. That's the biggest complaint and something that holds back inexperienced mountaineers on their first guided trips. Tripping and constantly catching an edge takes a lot of energy, then you also dislodge rocks on the fellows below you - not cool! RMI go at faster pace than other guided groups, so if they see you falling behind they usually turn you back.
Third, check out all the threads about Rainier clothing - there are many on these forums. Figure out the best layering system. I see guided climbers carrying 50+ pound of huge packs as if they're going on an expedition - while they don't even have to carry a tent or cooking equipment or ropes!
Fourth, on your climb, bring foods you like - you have a luxury of guided services, so you're not constrained by weight you can carry
If you haven't already, go backpacking (at least 2 nights) and figure out what works and what doesn't food-wise.
Good luck and have fun! If you decide you like it and want to stick with it, you'll already have most of the gear. If not, sell them here - more bargains for us