Hi Fred and congrats on getting your new plot.
I personally would select to grow rhubarb, raspberries and possibly globe artichokes in your wetter end of the plot. However, I would grow them in little hills of soil, so they aren't completely immersed. Not so sure about fruit trees - will leave that one to someone else.
It has been a very wet spring this year, so it might just be that your plot has suffered more than usual. If you find that your plot doesn't seem to dry out much - raised beds might be in order, I must admit, I use these on my plot for this reason and lost my garlic and onion to white rot in the beds before I created raised beds - although not caused primarily by wet soil, I don't think it helped. Although I introduced loads of manure and grit into the beds, I had to eventually create raised beds to alleviate the issue - this is the first year growing the alliums in the raised beds so fingers crossed I might have more luck.
I think Yorkie is right - you can't beat talking to the other plotholders to get a better idea of the usual state of the plot. Some people suggest digging out a ditch and filling with stones to create a drain on the plot too.
If you don't like chemicals - why not read up about lasagne gardening? I started my plot this way and, provided you loosen the soil before covering with layers, you may find it better for your drainage issues (as well as stifling the weeds somewhat). My plot suffers from bindweed, dock and couch and I would say that 90% of the weeds were killed off by creating the beds using the lasagne method, with the rest dealt with individually.
Most importantly, don't beat yourself up about getting it all done. Give yourself some time to enjoy it too. We only did two beds initially using the lasagne method and planted with strawberries, cabbages, beetroot, chard and squashes of varying types so we had plenty to harvest, then did the rest over time after that.