As someone who has worn suits daily for years, I had to come out of lurker mode on this one as I actually feel like I *might* be able to offer helpful comments. You have already received much good advice.
JCrew Super 120s is good quality stretch wool-- not top of the line but soft and fairly wrinkle-resistant. Top of the line wool fabrics are really incredible, but you pay for it. I would not buy a cotton suit as your first suit. There is a place for them in a suiting wardrobe but they are inappropriate in winter and wrinkle easily. Avoid polyester in ANY form-- it will not have mileage.
There are plenty of custom tailors that tour major US cities from China/HK regularly and many are willing to do women's suits. But, I've found that the same money spent on a off-the-rack suit yields better results. My one caveat is if you have a suit you want duplicated. YMMV, especially if you are hard to fit. JCrew does have a more "curvy" fit than Bennetton, and I've found them similar to BR in fit. I am less impressed by BR's fabric quality and details, especially jacket lining. I also like Theory and find Bloomies has by far the best suit department of the major stores I frequent. Brooks Bros can work if you want conservative. Avoid AT, especially the tri-acetate black mix-n-match pieces. I have a bleak period in my personal fashion history linked to these pieces and want to save you that. You say you are frugal: I have a friend who does well on eBay-- buying lots from women who have left the workforce or have moved to a more casual workplace. Some TJ Maxx/Marshalls have good selections, usually the city center ones.
You can get pants and skirts altered more easily and cheaply than jackets. But, I'd be very hesitant to order a non-returnable suit if you are not very familiar with the fit of the brand's jackets. Button placement, lapel width, jacket length have a big impact on a suit's final look and are hard to judge from pictures. I have tried on almost every JCrew suit for the past several seasons, so I feel comfortable ordering them on clearance as their standard styles do not change significantly.
I would advise you to think about what you really want a suit for-- funerals? interviews? spouse at business dinners? These, to me, suggest differences in what you are looking for in a suit-- color, conservatism, classic or with some "trendy" details like a peplum jacket, skirt/pants.
FWIW, my personal experience. Over the years, I've found charcoal gray suits are my workhorses. Black seems too dark on some occassions, especially summer, even with fun shoes and accessories. Navy makes me feel like a flight attendant, but I travel a lot. Browns seem harder to find nice blouses/shells to coordinate with. And, my coloring probably plays a part. I much prefer a pants suit to a skirt suit but both are widely acceptable even in professional settings and your choice will depend on body type, climate, preference in heel height, amount of travel you will do in a suit (pants work far better in planes-- cannot tell you the number of hose I have snagged on the velcro at the front of the seat that holds in the lifejacket).
Can't wait to see what you try!