I have two trailers: This one is good for shopping and camping, but not so good for taking rubbish to the tip because of its limited capacity.
Bike Cargo Trailer Bicycle Pannier Storage Bag Single 16" Wheel Colour Choice | eBay
Even with fairly large loads, you hardly know it's there. You can forget about it once you're going because it follows exactly the track of the bike and is narrower. It has quick release locking clamps that fit to the rear axle. You have to have the supplied spigots mounted to your bike permanently. They supply a skewer with the spigots on for a quick-release rear wheel, and spigots with a 10mm thread to use instead of normal wheel nuts, so they won't fit if you have a rear motor, but if you have enough thread on your axle, you could make a couple of short plates with two 10mm holes so that you can bolt the spigots just behind the axle. It only takes a few seconds to securely clip the trailer on/off
I also have a raleigh two-wheeled trailer for two small kids that I use for larger stuff. Likewise it works very well but you have to be careful not to hit the wheels when you go through bollards etc. It has a clamp that clamps to the nearside chainstay but it's only secure on traditional chainstays. Modern ones can be any shape. I can just get it on my Giant NRS, but I secure it with two study cable-ties in a cross pattern to make sure it can't come off.
The single-wheeled one is much better to use than the larger one by a long way. Only problem is capacity. You can get two bin bags of stuff in it with a cargo net over the top to hold it in place. Without a cargo net, one bin bag.
Other two wheel trailers have a short arm that bolts to the axle, so if you go for one like that, make sure you have enough spare thread on the nearside.