I'd reccommend Gem Squash (Jamie calls them 'cricket ball squash' in his book which gives you an idea about their size).
Reasons:
They taste good (although there are other squash with better flavour) and can be eaten young as spherical courgettes or allowed to mature when the flesh goes dark yellow and the skin very hard (how I harvest them). Like this they will store until mid-winter (never grown enough to go further) - I expect at least 10 mature squash per plant, and plant enough to be able to harvest 100-150 in about 15sqm.
Technically they are a summer squash (in the same group as marrows/courgettes etc), not a winter squash. This means that they ripen and mature earlier on in the season so they are easy to grow, with no worries about them developing a decent flavour before the first frosts (eg compare this with butternut).
They are very 'rambling' in habit. I plant my broad beans in treble rows with a 3" of clear ground between. The squash then get 'island planted' along these paths. They remain small enough to step over whilst cropping early sown/over wintered beans. Then when I cut down the spent beans (without digging them in) I spread a good thick organic mulch over the whole area and just let the gems take over. Have been doing this for the last 4 years and usually get 15 squash per plant.
I'd strongly suggest that you don't plant them amongst summer maturing crops (eg sweet corn/three sisters planting regimens) as they will go down with powdery mildew, whereas this doesn't seem a problem if they are left in the open until late September/October most years. Having said this if there is an adjacent sweetcorn bed I do let them ramble through, but accept that these plants may have early-season disease issues.
SS