You'll find plenty of 1 bedroom apartments under 1000€ in Lisbon on AirBnB
The long term rate is usually around 500€, so 700-900€ for 1 month on a nice, renovated and cozy apartment isn't that far off.
Public transport is good in Lisbon, maybe a bit crowded. (I'm not the best person to comment, I drive to everywhere here )
Plus, Lisbon is still sunny and lovely in October, it usually only starts raining in November.