What main roads will you need to travel on? Your journey is very specific but there may be some major roads that a few people on here travel on.
I can't help too specifically as I travel from South West Sheffield to Doncaster and vice versa but I do travel on the M1 so could help there.
As long as you check there's no traffic on the M1 its useful fine, busy, but fine. Its 50 in the morning from the Rotherham/Sheffield junction and up past Meadowhall but I'm not sure where the 50 stops.
Coming out of Sheffield to go onto Parkway is an absolute nightmare pre-lockdown. Always going to be queuing after the Catcliffe Morrisons junction after around 3pm. Travelling into Sheffield in a morning there are always big queues there too but if you work in North Sheffield I presume you wouldn't need to go to the bottom of parkway if at all.
There are lots of affordable areas surrounding North Sheffield and wider, I don't believe that Wombwell is the only place you can afford to live in the entirety of South Yorkshire. Doncaster has nice areas- Tickhill, Bawtry etc. Rotherham has Wickersley, Whiston, Ravenfield etc. Sheffield has Eckington, Sothall, Beighton, Killamarsh, Wales, South Anston