We did ours the same way though with well-rotted horse manure. They worked a treat.
cardboard is good ,
carpet is ace but avoid man made fibres, wool is great and even adds nitrogen if it is a longish term job
one advantage of clear plastic is that once the no dig feed and clean solarisation ferment and worm work is done a few big hoops turns it into a big cloche or several small cloches for an early start with stuff like broad beans , salads ,alliums etc
the plant through with high feeder copraphiles this summer and swap to autumn planted stuff for spring under it works well
i know you said no dig but a little bit of dig and prep where you are planting seeds or young plants often helps a lot.
re manure . if i was starting with a grassed/"weedy" area and wanted good growing soil i would obtain a layer about 150 mm deep for the first year and add as much as possible under and around plantings after that.
that might seem like a lot but you want a veg bed.
i know you said no dig but if the land is compacted one dig at least 2 spits deep and adding lots of manure and grit if needed is good, after that just top up with manure during the rotation of crop types
worms are your chum and they are not keen on compacted soil. if the soil is stirred a bit they are far happier turning "wasteland" and manure into a nice growing medium.
even just deep spiking it with a fork before adding the manure or chewing it up with a Rotavator will make it easier for worms in a compacted soil
||we all forgot gruntavators, a few pigs will sort the weeds from a plot ever so quickly after that enjoy a bacon butty and watch the plants grow.|
I wondered if you may prefer the alternative of raised beds. This gives you permanent pathways round the garden and saves a bit on your back, but also gives beds you are in control of for each season, and you control the rotation better-a few extra plants won't fit then you do a swap rather than add them into another bed which is how you would do an 'open' garden. You can also put up a cover over selected beds, and so put things in sooner, or protect from the early frosts. Those first really early potatoes-yum. A covered bed also allows you to be growing into the autumn when the first frosts appear. I made my first cover frames out of wood but if doing it today I would use blue flexible hose pipe, which doesn't attack the polythene cover like wood- trust me!
Another advantage with individual beds is that you don't step back into something else to admire your efforts-been there a few times. Indeed you shouldn't get compaction from human feet at all. Years ago I did a long covered half bed the length of my veg patch 4ft wide and around 40ft long, half in early potatoes followed by early sprouts, Peer Gynt I think the sprouts were; and half in main crop potatoes, not covered followed by purple sprouting for the following spring. 3ft is plenty for a permanent walkway-wheel barrow and a bit!
Against this it costs a few bob to set it up. But if you go to any large steel factory they are often only too pleased to get rid of pallets that are not returned, I worked in such a place and had a field day!
||We have raised beds and they are a lot easier to work. If you use weed suppressing membrane on the paths, extend it slightly under the beds though. The sides will rot, so choose carefully. Western red ceder isn't bad nor is oak, but would expect, unless you were very lucky, that pallet wood would need replacing every few years.|
||Pallets are cheap from those places that don't return them, MR; a few of the local places by me have pallets outside for anyone to go and collect-I do as well, it is better, cleaner wood than ours!|
||I agree pallet wood is the cheapest, but unless you pick the right stuff, you will be remaking your raised beds every year or two.|