Either will work. I did it on conti speed cross which is a 35mm file tread. Other half did it on 28mm marathon supremes with mudguards and didn't have any issues.
Got a pair of 32c Vitoria XNs that should do it nicely - file tread with knobbly shoulders for the field sections
Got a pair of 32c Vitoria XNs that should do it nicely - file tread with knobbly shoulders for the field sections