Welcome, NateH777. I've dealt with all three that you mention.
Top Shelf is an excellent tailor but charges top dollar for their work. I've never had anything made by them, but I'd trust them to do a credible job (they make suits and shirts if I remember correctly).
Hubert White has a very impressive selection and a knowledgeable staff. I've bought several things from them, nearly all on sale. They are willing to assist you but a bit on the cold side if you don't work in the IDS Building and carry a multi-thousand dollar clothing budget with you. Their in-house tailoring is excellent, but I've only used it on stuff I've bought from them and never brought in anything of my own. If you can afford it, you'll end up with good products and generally good advice.
Heimie's Haberdashery is a joke, staffed by incompetent salesmen trying to sell subpar brands. All of their suiting, even MTM, is half-canvassed or fused, and their cuts are dated and lackluster. I'd stay away.
You didn't mention Martin Patrick 3, which has a well curated collection and a knowledgeable staff but at staggering prices for their tailored stuff.
If you plan to buy most of your clothing online and want a good tailor who's not affiliated with any of these places, send me a PM and I'll send you to my tailor, who is a perfectionist in the best sense of the word. She's fixed the errors of many other Twin Cities "tailors" over the past couple of years.