At Sheffield you will encounter Stagecoach, First and TM Travel buses
There's also Hulleys of Baslow (on Peak District services - 271/ 272/ 273/ 274/ 275) and Sheffield Community Transport (though SCT don't serve the Interchange IIRC, if that was what you were meaning.
Who even goes to Sheffield Interchange these days?? Meadowhall is the new message.
So I'm guessing Sheffield interchange isn't the place to go then?
It's very quiet, I think most services have moved out over the years. I remember when they demolished half of it about 10 years ago they struggled to fit all remaining services in the other half. Now you could almost layover for half an hour on a live stand.
Around Castle Square by the tram tracks is probably the busiest spot. The top of The Moor by all the roadworks is probably another good spot to see lots.
Aye, Sheffield Interchange was busy in the '90s but slowly got quieter and quieter - partly because it's nowhere near the main shopping area, partly because we've lost some of the "out of town" bus services (Huddersfield, Bradford, Leeds, Stoke, Grimsby, Hull, Worksop...), partly because frequent urban routes have been combined (e.g. the 60 to the Hallamshire and the 41 to Crystal Peaks both ran every six minutes or so, so layovers at the Interchange were common, but now there's the 120 linking both sides of town).
The FreeBee was every seven minutes (in theory!), but was cut back, along with similar free city centre services in comparable places.
The "recent" Partnership changes (October 2015) have meant even fewer services around the Interchange area (e.g. the 47/48 and 53 used to run up and down Flat Street fairly often but the replacement services either serve the main shopping area or only run past in one direction).
So, for variety, I'd go near Castle Square Tram Stop (north end of town) or Debenhams (south end of town).
Waingate can be good for photos (due to the hill), Hillsborough can be fairly busy at times. I wouldn't bother with Meadowhall as there's not much there that doesn't come into central Sheffield (esp given the way that Rotherham services interwork into central Sheffield, as do the two "ring road" services, the 18 and 38). The only advantage of Meadowhall is Megabus (which doesn't serve central Sheffield).
The tram is the reason there's (virtually?) no Stagecoach buses at Meadowhall.
I could be wrong, but I think that the Megabus is the only Stagecoach service to have served Meadowhall, after the initial retrenchment when they took over Yorkshire Traction (Tracky used to run some of their services from the Dearne Valley to Rotherham through to Meadowhall for many years, but it didn't last long after the Stagecoach takeover, and they've not been back, despite the provocation from First on the "22" corridor).