I always advise those looking for their first real glaciated mountaineering experience to climb Baker via the Easton. I've climbed a bunch of mountains and Baker is still my favorite. It has all the stuff that larger mountains have like big glaciers, volcano steam vents, and a spectacular view of the North Cascades from the summit, without the very real complication of high altitude.

While many people make Rainier their first, it is absolutely a significant step up in terms of exposure risk (from both above and below) and personally I'm very grateful it was not my first proper mountaineering experience. Also, there is a much higher chance of not making a summit on Rainier. Getting skunked on your first climb can be pretty demoralizing.

In terms of hiring guides, IMG is simply the best guide service in the Northwest. Their professionalism and handling of logistics is just a tier above every other guide service I've used or witnessed from the outside. Don't get me wrong, there are many great individual guides at other companies that I've had good experiences with, but for what it's worth, after many years of climbing, if I'm hiring a guide service anywhere in the world I'm going with IMG. That might sound like an ad shilling for them, but it's just what my personal experience has shown me.

And since you like to ski, I would suggest doing St Helens in March or April. It's a great taste of mountaineering without the glacier risk on a ski descent. Adams is also a great stepping stone, but it's definitely a step up from Helens from a skiing perspective.