The chromogenic B&W films mentioned above are easily processed at one-hour labs and cost the same as having C-41 done. I just have mine processed, cut, and sleeved - I do my own scanning and don't order prints. Cost is $2 USD at Walgreens.
As to using one of the various chromogenic films (Kodak & Ilford) over using standard C-41 and then desaturating in PS, I could not tell you which is better. I note that some C-41 color films are pretty inexpensive, while C-41 B&W films tend be a bit pricier. Economically, it might make some sense to buy cheap color film and convert it to B&W in PS later.
In addition, if you scan your own or have it scanned for you and choose to do color film, you can use channel mixing and various other tools to obtain some of the effects that you would otherwise get by using actual B&W style filters (red, orange, yellow, green, blue) on true B&W film. If you scan C-41 B&W (or true B&W for that matter), you can't apply filter equivalents through PS later on - the color information is not there to operate on.
I guess if my choice were to be C-41 color or C-41 B&W, I'd choose the cheaper color film and gain the added advantages of PS adjustments as well. But you feel otherwise.
Best Regards,
Bill Mattocks