I agree that 4 x 8'x4' beds is not a lot of space, so I personally would choose to only grow crops that have "best value", for me that would be the ones that tick the most boxes for
high yielding
expensive in shops
best flavour (which would including growing varieties, even low yielding, that are not available to buy in shops - thin skinned Tomatoes
for example, or Sweetcorn)
I think you could take a different view on Rotation. With beds of that size if you had to you could replace the soil. I have read (pretty sure it was Joy Larkcom) that one way, in a small plot, is to monocrop a single bed year after year until you get disease and then move it. I don't do this because, to me, one of the reasons for rotation is so that different crops demand different nutrients from the soil, year on year and the soil has time to recover and be replenished by manuring / liming etc.
However, I wouldn't follow Potatoes with Tomatoes - too much risk that some disease had started brewing in the Spuds and then wiped out the Toms.
An allotment - originally sized to be the space needed to grow food for a family - is 250 sq.m., so allowing 2' path between your beds then your plot is going to be about 18 sq.m., hence my suggestions would be that you concentrate on some specifics.
If you are not familiar with it you might like to look at "Square foot gardening" which is a planting technique designed to get maximum productivity from a small plot.
For me Spuds would be out - too much space for too little yield for a very low cost product - but if you are keen to have early First Early potatoes you might like to consider growing them in containers (there are special bags available, which have handy handles but also fold up flat when not in use). Yield is low (compared to in the ground) but the compost you use to grow them in goes on the garden, so that's a bonus of sorts