In my veg plot I have had to remove rubble, black polythene and many perennial weeds. The previous occupiers tended to lay new soil over the weeds and plant on top. This was surprisingly successful but in the long run makes for a very messy garden. As a result I've had to spend hours during my weekend simply digging up weeds and rubbish, putting it in a wheelbarrow and taking it to a skip/ compost heap. Unfortunately, it sounds as though you might have to do the same thing. Tenacious bushes can be got rid of by cutting them down and digging up the roots but it is a long job. If you have rushes and horsetail, they are there because, as you say, your land is boggy. Short of putting in a new drainage system, it is likely to remain that way and weeds that like those conditions will return.
Have a look at our advice on dealing with horsetail at:
As you can see, constant cutting of the top will weaken the plant as it can't photosynthesise without leaves. This is a long term strategy - you would need to keep coming back to it again and again.
As before, I do recommend planting things that you like if you can find space. Willows and Alders love boggy ground and are very attractive. The theory is that they could out-compete the things you don't like.
Please also see our list of plants suitable for boggy soil at:
However do make sure any plants you pick will be hardy in your area.
One thing that has made working in my veg plot more fun in difficult times is doing it with friends. I hope you can find some good company to dig and cart alongside you.
Please do let us know how it goes.