Do you think I should just learn on rentals for a year while I lower my wait and raise my skill level before I purchase skates?
If you have tried out the sport and decided you want to learn it, you really need your own boots. You don't need high-end expensive boots, but you will progress faster - and be much more comfortable! - in your own boots.
The person who measures and sharpens figure skates at my rink says that he primarily sells Riedells.
Would you suggest any of those?
There are many reputable makers to choose from, including Riedell. However, the most important thing is to get a boot that fits properly - an ill-fitting boot will hinder your progress, cause you discomfort or pain, and may cause you lasting injury. The first thing you need to consider when buying boots, is which *brand* of boot fits your feet best. There is no one right boot for everyone; every maker has a different last and each last fits differently. Some people will slide right into Riedells but couldn't wear Jacksons; others fit Jacksons right out of the box but couldn't wear Risport etc.
You mentioned that the Classique or Freestyle models would be better for my weight, but I'm a beginner, just starting basic lessons next month, won't the boot be too firm for me? Aren't they made for the higher-level skills?
If your foot is a "Jackson foot", I'd second/third/fourth everyone's of Freestyle or Classique. Both are rated stiffness 45, which is not really that stiff for a heavier adult. The main difference between them is that Freestyle has a leather sole while the Classique has a plastic sole with a riveted blade. The blade on the Classique is fine for beginners, but the plastic sole means it is very difficult to reset if your foot alignment means the blade needs moving (most skate pros won't/can't move blades on plastic soles).
With a budget of ~ $150, you might luck into a pair of Classiques on sale. As a beginner, you might also consider looking into secondhand boots - you can often end up with a nice pair of boots for much less than new, and someone's already done the hard work of breaking them in. If you do go the secondhand route, take someone competent with you to be sure you don't end up with a lemon which is completely broken down or has a twisted sole etc.
Don't - whatever you do - buy the $50 Walmart jobs.