I don't really like strimmers - they frighten me! Our plot is full of slow worms and I am sure we would kill loads had we used a strimmer.
We started by just cutting back the growth with shears, pulling up the nettles and larger weeds as we went and putting them into old buckets of water to start creating nettle and weed tea to feed plants with.
We then invested in a roll of weed suppressant to stop stuff growing before we could clear it (carpet is banned now on the site). I bought it online - it was about £30 for 100m.
We roughly marked out the beds and actually didn't clear anything - we used the lasagne gardening approach and simply begged cardboard from neighbours, shops and freecycle and used this to cover the weeds. We then piled farmyard manure, grass clippings (again from free sources), shredded paper, newspaper, etc. Then topped with compost (the only thing we bought other than the weed suppressant). We then planted straight into this. As the more pernicious weeds grew through, these were pulled out.
We did take over the plot in June so the soil was rock hard and impossible to dig (barely any had been previously cultivated for as long as anyone could remember). However, I would still use this method at this time of year too - planting onions and garlic or simply missing out the compost and leaving the beds covered in weed suppressant ready for spring, adding compost on top come spring before planting.
Later, we double dug other beds, adding manure, etc yet the ones that have performed the best by far are the lasagne beds, so we are now recreating the lasagne approach on the previously dug beds.
Just to demonsrate how bad our plot was - it took us two months to find carpet under one part of the plot because it was so overgrown!