Welcome to the site blancmaison.
Your weeds sound like a potent mix, I do not use glyphosphate (its your choice, and it does kill weeds!) but covering with mulch takes longer and if you can get it on as soon as possible, there is still barely enough time for the roots of vigorous perennial weeds to have been exhausted by next spring. However they will be massively weakened. Maybe leave the mulch on until May or June, before planting up for the summer and autumn.
Soil quality will be helped by spreading compost/manure either now, before mulching, or in the spring when mulch is removed. This also helps to conserve moisture, improve drainage and in weed control
Soil seems not to mind being under black plastic but a breathing mulch such as Mypex or cardboard does feel like a healthier option. I think there is no absolute right or wrong, do the best you can with whatever materials you can muster, and the soil will repay you for not being significantly disturbed.