From the train station, head right-ish and walk through the bus station to the furthest corner (past the WH Smith etc) and you’ll find a hill called Flat Street (this is Sheffield, not everything makes sense!)
That’s where the Stagecoach 43/44 terminate (near the bingo hall), the Dronfield/ Chesterfield routes
Alternatively, if you don’t mind a slightly longer walk (for a much better choice of buses), follow the main crowds left-ish out of the station, past the “blade” sculpture/ fountains towards The Howard, the Tudor-style pub, and up Howard Street (a pedestrianised hill, by some of the Sheffield Hallam University buildings)
At the top of the hill you’ll find Arundel Gate, a busy road through the centre of the city (post-war Sheffield decided to build big dual carriageways through the city centre, but these have been calmed down over the years) - there’s a bus stop there - AG10 - for the 20 (First, Hemsworth), 24 (First, Lowedges), 25 (Stagecoach, Bradway) and aforementioned 43/44, which all go past Rails
On your way out of town, you’ll cross the River Sheaf then go under the Midland Main Line… ring the bell one stop later (once you’ve gone past Ponsford furniture shop)
There’s a few independent shops/ pubs/ cafes on the same side as Rails, there’s a Lidl/ B&M on the other side of the road, depending on whether you need anything whilst you’re in that part of town
Maximum bus fares should currently be £2 under the PTE/ Mayoral scheme, but I don’t know if that’ll be the case when you visit… can’t promise!
(There’s also the Stagecoach X17 to Chesterfield/ Matlock; that’s not as frequent/ limited stop, but it is faster than the other routes, and it’s Stagecoach Gold spec)