What to wear when you do tai chi is a common question for (and from) beginners. Loose, comfortable clothing is typical. Shoes are perhaps more important for tai chi and martial art attire. Flat, low volume shoes are the best.
I prefer something I can wear in practice and on the street, but it’s not easy to find a good compromise. A good and light indoor practice shoe will fall apart pretty quickly out of doors. I found a pretty good middle ground with the Bushido (https://bushidomartialarts.com/products/bushido-shoe) that I have gotten at Valley Martial Arts in Glendale, California. The soles in the front are flat, smooth (real) rubber and the rear has a herringbone type of tread.z The drawback for these is that they have a mesh construction over the top, so dust and sand can get inside. I actually don’t have much trouble with that and I still like them for their durability and lightness.
Of course, the ol’ standby from Shanghai, Feiyue (“flying forward”), is probably one of those shoes that every martial artist owns at some point. Bushido makes a Feiyue type shoe with their name on it that sells for $20. I find them to be hot in summer and cold in winter, but I still have a pair and where them around the house all the time to practice. Easy to get at Amazon (http://www.amazon.com/Tiger-Claw-Feiyue-Martial-Shoes).
I’ve had Tiger Claw shoes, too, which lasted a long time (tigerclaw.com). They sport a cool Chinese tiger character on the top. They have only one model and two colors: black and white)
The Onitsuka Tiger by Asics shoe is very close to my favorite. They are long-lasting and you can wear them all the time. There are many models to choose from, including suede and leather. The suede versions get dirty rather easily, but you can wipe them down when you need to with soapy water, a brush and rag. Check it out and let me know what you think. I bought mine from Amazon but you can get them at Zappos, but they cost $75 now.
Adidas makes a martial art shoe that I wore when I first began studying tai chi. I like them because they lasted so long and they have a slightly higher top than other martial arts shoes. However, they are not lace up. The have an elastic, slip-on feature that’s cool, but I prefer lace up because I can tie them as tight or loose as I like. Still, the Adidas shoe is pretty good. Unfortunately, they were sold out a the Martial Arts Mart last I checked (http://www.martialartsmart.com/a90-sk.html).
Skechers makes some shoes I’ve seen others wearing and I think they look really good, but I’ve never tried them out and I think they are overpriced. I’ve seen some Merrells that are made for outdoor trail running that look great, but there again, expensive.
This year (2017) I discovered some great new shoes on Amazon < https://www.amazon.com/gp/product/B01HFWHGJI/ref=oh_aui_detailpage_o01_s00?ie=UTF8&psc=1> for $18.00. I like them. I use them only for indoor tai chi, not street walking. They have very soft insoles that I find extremely comfortable. The brand is one I had never seen before. The title on Amazon goes like this: TimeBus Chinese Traditional Martial Arts Tai Chi Kung Fu Yoga Walking Jogging Driving Shoes, Breathable Soft & Comfortable, Black. Funny.
Mingren makes a cheap canvas-based shoe that I wear regularly. I use them for tai chi and street, and I don’t care if they’re dirty, because they only cost $18 (Amazon—YUNEE-MINGREN-Athletic-Lightweight).
You’ve probably gathered that there are a lot of options for martial arts shoes out there. Choosing can be a hassle, so my rule of thumb is go with as inexpensive as possible, see what works best for you, especially if you’re just beginning. Then go from there. I still get the cheap stuff myself.