The point with your book's advice to look around and see what's growing well, is to help you choose what grows well in your area, so you start off with everday veg, nothing fancy and have some encouraging success. Then you try out other things, one or two a year, and see how they do for you, in your area and on your plot, which will have its own microclimate, soil etc. Your way of growing your veg, such as where you start them off, that is in a propagator, in pots or modules in the house, in an unheated greenhouse, or directly into the soil, will all have a bearing on your success.
When you say you can't grow French beans but you can grow dwarf beans, what exactly do you mean? The two climbing beans are runners and French, dwarf beans are also French.
It's difficult to know what might be the cause of your problems without also knowing the details of all the variables mentioned above.
Here, I can't grow outside things such as sweetcorn, climbing or dwarf French beans, or runner beans, and in most years lettuce and squashes don't do well outside either. French beans in particular are very subject to cold soils, which rot off the seeds. The funny way to test soil temp is to sit on the soil with a bare bum, but you can test it, a couple of inches down, with the inside of your wrist - if it's comfortable, then your soil is ok for beans. Climbing beans and sweetcorn are very susceptible to cold wind, which is what has done for ours in the past (I start them off in pots under cover, so soil temp is fine). So I grow these crops in the polytunnel. 300' down the hill, other people can grow these crops outside.
Cucumbers are quite complicated to grow, especially starting them off. They are very temp susceptible, they hate having soggy roots, and any set-back when they are small will affect their productivity and survival later.
First you have to be growing the right variety ie for indoor growing in a heated greenhouse, in an unheated polytunnel, or outdoors. All female varieties are more convenient to grow as you don't have to pick off the male flowers. They like a slightly moist, draught free air quality, but not humid. I tend to make a surround for my cucumbers of horticultural fleece, to keep off the draughts in my polytunnel. They grow very well most years.