For anything that will occupy the ground for a long period, trees fruit asparagus etc the real enemy is perennial weeds. So your plans to eliminate these as far as possible is exactly correct. The problem with grass is that some varieties are perennial weeds in their own right.
You really need to fork through a good area of the grasses and identify which types you are dealing with. Couch grass for example is easily recognised, but if you do find perennial grasses in the mix - regrettably - it will be much harder work to remove these using only a garden fork. No perennials? Just dig in.
If you find lots of perennial grasses you may need to consider herbicide to clear the area before planting. This is not an option I would choose, but my soil is comparatively light and several years hard work has allowed me to clear my plots of perennials apart from a small patch of bindweed that re invades each year from a neighbour's plot who seems happy to ignore it rather than try to remove it.
Good luck. Overall, fruit returns some of the best value for time and effort that you can get from an allotment.