What is your mountaineering or hiking experience? You are in Ohio, right? Keep in mind that (it sounds like) replies are coming from experienced CO mountaineers. I'd suggest working up to Rainier by doing some smaller peaks for months or years.
If you want to do a cool big peak with a guide, how about Mount Hood, 11,239'. Plenty tough, but way easier than Rainier.
Then Mount Adams, 12,276'.
Mt Shasta is awesome, 14,179', easiest routes are relatively non-technical, crampons typically needed. Its been years, but my recollection of Avalanche gulch is non-crevassed; mainly a big snow hike, with a boot trail in already (unless its dumping
. This is a great ski, so many lines.
Mt Elbert is a CO 14er that is more of a trail hike, that you could do without a guide, if you are in good shape, acclimatize, and plan well. This would give you a taste of 14,000'+, while the others involve more mountaineering (using crampons, ice axe, route-finding, weather prediction ...)
14ers.com • Mt. Elbert | Route Descriptions
Those 3 or 4 peaks above would be a great way to work up to Rainier, and they are all awesome climbs by themselves. Take up rock climbing in a gym too, to get over your fear of heights, learn rope work, etc.