Best material to cover resting beds

Two options, depending on what you prefer. The soil here is heavy clay, albeit improved now with years or organic matter but still clay
1. Thick black plastic. I use this as it stops the beds getting waterlogged in Winter, stops nutrients from leaching, prevents anything that germinates from growing past seedling stage and lasts for years. I have some pieces 9 years old. It does not prevent air from getting to the soil (as some folk have told me it will) and in the Spring the round is good to go. Worms are happy in the sheltered ground too.

2. Heavy weight landscape fabric. More expensive, frays along cut edges unless you heat seal it and is porous, so if you have very dry soil this could be for you, or if it is a long term coverage this is better. I used it to cover the ground where the second polytunnel was going and it was down for 18m... excellent when ti was rolled back as there was perfect bare soil. My plot neighbour covered a section of her plot for a year and the only plant visible were some yellowing looking strands of bindweed.
This an be planted through too, of course, if you cut holes in it

Both need to be fully light proof, and both need to be properly weighted down (I use buckets of stones and planks of wood) so they don't blow away

Hope that helps

Depending on how long the bed is going to be covered I am a big fan of grass clippings. Generally I do this later in the year and find it acts as a good weed suppressant as well as a soil conditioner, there are always loads more worms in the soil covered this way and it is far easier to dig. I usually put on a 5-6 inch deep layer and leave over winter. This time of year I think i would tend more toward fast growing green manures.   

I use cardboard, weighted down with bits of old wood, once it has been wet for a while it tends to 'stick' of it's own accord.

I also use green manures.  But I do so sparingly, I have a tight budget and even a pack of seeds has to be carefully thought about.