I'd properly develop and expose for normal contrast, and add the contrast when printing. Then you can have the potential for multiple contrasts for different uses. Scanning will work better with normal contrast negatives, at least with an epson. Some scenes you might want a little more shadow or highlight detail later on, which might not be as easy if the negatives are high contrast. Just my personal style. I've mostly used tmy2 and d76 or xtol for random convenient shooting. Tmy2 is more expensive than the various low budget tri-x clones, but it's very consistent quality and less grainy.
I would advocate using Tri-X @ ISO 400 for daytime street photography, developed in D-76 1:1. This works very well for me - no issues or complaints.
If you need more speed than ISO 400, Tri -X pushed to ISO 1600 and developed at ISO 1600 looks really nice - to my eye, at least. Straight work prints at 8"x10" size show nice smooth grain with a bit of a loss in contrast - noticeable but not objectionable. The contrast loss can be addressed in printing.
If you want finer grain than Tri-X, give Fuji Acros ISO 100 a test drive. Acros is not as forgiving as Tri-X is, though.