It looks like you could make this with mostly 18mm MDF with no need for a timber frame at all. If you wanted to make it bomb proof you could glue some 2x2 behind the corner joints but I don’t think it’s really necessary if you use decent screws. Glue and screw it all together and then cut strips of 6mm MDF which you glue on to create the panels and in the process cover the assembly screws as filling over screw heads can be a problem. For the seat I’d double up the MDF to make it 36mm. A few joints along the short dimension won’t matter so you can use up what MDF you have left for the lower piece as you won’t be able to see it once the seat is in place.

It would be worthwhile making a cutting list and getting as much of the MDF cut to size as possible unless you have access to machinery. And be careful when cutting MDF, wear a mask, as the dust can do you no good if you breathe it in.